Write in Standard Form 3y^2+8x+24y+40=0

$3 y^{2} + 8 x + 24 y + 40 = 0$

Solve for $y$ .

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 3$ , $b = 24$ , and $c = 8 x + 40$ into the quadratic formula and solve for $y$ .

$\frac{- 24 \pm \sqrt{24^{2} - 4 \cdot (3 \cdot (8 x + 40))}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

Raise $24$ to the power of $2$ .

$y = \frac{- 24 \pm \sqrt{576 - 4 \cdot 3 \cdot (8 x + 40)}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$y = \frac{- 24 \pm \sqrt{576 - 12 \cdot (8 x + 40)}}{2 \cdot 3}$

Apply the distributive property.

$y = \frac{- 24 \pm \sqrt{576 - 12 (8 x) - 12 \cdot 40}}{2 \cdot 3}$

Multiply $8$ by $- 12$ .

$y = \frac{- 24 \pm \sqrt{576 - 96 x - 12 \cdot 40}}{2 \cdot 3}$

Multiply $- 12$ by $40$ .

$y = \frac{- 24 \pm \sqrt{576 - 96 x - 480}}{2 \cdot 3}$

Subtract $480$ from $576$ .

$y = \frac{- 24 \pm \sqrt{- 96 x + 96}}{2 \cdot 3}$

Factor $96$ out of $- 96 x + 96$ .

Factor $96$ out of $- 96 x$ .

$y = \frac{- 24 \pm \sqrt{96 (- x) + 96}}{2 \cdot 3}$

Factor $96$ out of $96$ .

$y = \frac{- 24 \pm \sqrt{96 (- x) + 96 (1)}}{2 \cdot 3}$

Factor $96$ out of $96 (- x) + 96 (1)$ .

$y = \frac{- 24 \pm \sqrt{96 (- x + 1)}}{2 \cdot 3}$

Rewrite $96 (- x + 1)$ as ${(2^{2})}^{2} \cdot (6 (- x + 1))$ .

Factor $16$ out of $96$ .

$y = \frac{- 24 \pm \sqrt{16 (6) (- x + 1)}}{2 \cdot 3}$

Rewrite $16$ as $4^{2}$ .

$y = \frac{- 24 \pm \sqrt{4^{2} \cdot (6 (- x + 1))}}{2 \cdot 3}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{- 24 \pm \sqrt{{(2^{2})}^{2} \cdot (6 (- x + 1))}}{2 \cdot 3}$

Add parentheses.

$y = \frac{- 24 \pm \sqrt{{(2^{2})}^{2} \cdot (6 (- x + 1))}}{2 \cdot 3}$

Pull terms out from under the radical.

$y = \frac{- 24 \pm 2^{2} \sqrt{6 (- x + 1)}}{2 \cdot 3}$

Raise $2$ to the power of $2$ .

$y = \frac{- 24 \pm 4 \sqrt{6 (- x + 1)}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = \frac{- 24 \pm 4 \sqrt{6 (- x + 1)}}{6}$

Simplify $\frac{- 24 \pm 4 \sqrt{6 (- x + 1)}}{6}$ .

$y = \frac{- 12 \pm 2 \sqrt{6 (- x + 1)}}{3}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

Raise $24$ to the power of $2$ .

$y = \frac{- 24 \pm \sqrt{576 - 4 \cdot 3 \cdot (8 x + 40)}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$y = \frac{- 24 \pm \sqrt{576 - 12 \cdot (8 x + 40)}}{2 \cdot 3}$

Apply the distributive property.

$y = \frac{- 24 \pm \sqrt{576 - 12 (8 x) - 12 \cdot 40}}{2 \cdot 3}$

Multiply $8$ by $- 12$ .

$y = \frac{- 24 \pm \sqrt{576 - 96 x - 12 \cdot 40}}{2 \cdot 3}$

Multiply $- 12$ by $40$ .

$y = \frac{- 24 \pm \sqrt{576 - 96 x - 480}}{2 \cdot 3}$

Subtract $480$ from $576$ .

$y = \frac{- 24 \pm \sqrt{- 96 x + 96}}{2 \cdot 3}$

Factor $96$ out of $- 96 x + 96$ .

Factor $96$ out of $- 96 x$ .

$y = \frac{- 24 \pm \sqrt{96 (- x) + 96}}{2 \cdot 3}$

Factor $96$ out of $96$ .

$y = \frac{- 24 \pm \sqrt{96 (- x) + 96 (1)}}{2 \cdot 3}$

Factor $96$ out of $96 (- x) + 96 (1)$ .

$y = \frac{- 24 \pm \sqrt{96 (- x + 1)}}{2 \cdot 3}$

Rewrite $96 (- x + 1)$ as ${(2^{2})}^{2} \cdot (6 (- x + 1))$ .

Factor $16$ out of $96$ .

$y = \frac{- 24 \pm \sqrt{16 (6) (- x + 1)}}{2 \cdot 3}$

Rewrite $16$ as $4^{2}$ .

$y = \frac{- 24 \pm \sqrt{4^{2} \cdot (6 (- x + 1))}}{2 \cdot 3}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{- 24 \pm \sqrt{{(2^{2})}^{2} \cdot (6 (- x + 1))}}{2 \cdot 3}$

Add parentheses.

$y = \frac{- 24 \pm \sqrt{{(2^{2})}^{2} \cdot (6 (- x + 1))}}{2 \cdot 3}$

Pull terms out from under the radical.

$y = \frac{- 24 \pm 2^{2} \sqrt{6 (- x + 1)}}{2 \cdot 3}$

Raise $2$ to the power of $2$ .

$y = \frac{- 24 \pm 4 \sqrt{6 (- x + 1)}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = \frac{- 24 \pm 4 \sqrt{6 (- x + 1)}}{6}$

Simplify $\frac{- 24 \pm 4 \sqrt{6 (- x + 1)}}{6}$ .

$y = \frac{- 12 \pm 2 \sqrt{6 (- x + 1)}}{3}$

Change the $\pm$ to $+$ .

$y = \frac{- 12 + 2 \sqrt{6 (- x + 1)}}{3}$

Factor $2$ out of $- 12 + 2 \sqrt{6 (- x + 1)}$ .

Factor $2$ out of $- 12$ .

$y = \frac{2 \cdot - 6 + 2 \sqrt{6 (- x + 1)}}{3}$

Factor $2$ out of $2 \cdot - 6 + 2 \sqrt{6 (- x + 1)}$ .

$y = \frac{2 (- 6 + \sqrt{6 (- x + 1)})}{3}$

Rewrite $- 6$ as $- 1 (6)$ .

$y = \frac{2 (- 1 \cdot 6 + \sqrt{6 (- x + 1)})}{3}$

Factor $- 1$ out of $\sqrt{6 (- x + 1)}$ .

$y = \frac{2 (- 1 \cdot 6 - 1 (- \sqrt{6 (- x + 1)}))}{3}$

Factor $- 1$ out of $- 1 (6) - 1 (- \sqrt{6 (- x + 1)})$ .

$y = \frac{2 (- 1 (6 - \sqrt{6 (- x + 1)}))}{3}$

Move the negative in front of the fraction.

$y = - \frac{2 (6 - \sqrt{6 (- x + 1)})}{3}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

Raise $24$ to the power of $2$ .

$y = \frac{- 24 \pm \sqrt{576 - 4 \cdot 3 \cdot (8 x + 40)}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$y = \frac{- 24 \pm \sqrt{576 - 12 \cdot (8 x + 40)}}{2 \cdot 3}$

Apply the distributive property.

$y = \frac{- 24 \pm \sqrt{576 - 12 (8 x) - 12 \cdot 40}}{2 \cdot 3}$

Multiply $8$ by $- 12$ .

$y = \frac{- 24 \pm \sqrt{576 - 96 x - 12 \cdot 40}}{2 \cdot 3}$

Multiply $- 12$ by $40$ .

$y = \frac{- 24 \pm \sqrt{576 - 96 x - 480}}{2 \cdot 3}$

Subtract $480$ from $576$ .

$y = \frac{- 24 \pm \sqrt{- 96 x + 96}}{2 \cdot 3}$

Factor $96$ out of $- 96 x + 96$ .

Factor $96$ out of $- 96 x$ .

$y = \frac{- 24 \pm \sqrt{96 (- x) + 96}}{2 \cdot 3}$

Factor $96$ out of $96$ .

$y = \frac{- 24 \pm \sqrt{96 (- x) + 96 (1)}}{2 \cdot 3}$

Factor $96$ out of $96 (- x) + 96 (1)$ .

$y = \frac{- 24 \pm \sqrt{96 (- x + 1)}}{2 \cdot 3}$

Rewrite $96 (- x + 1)$ as ${(2^{2})}^{2} \cdot (6 (- x + 1))$ .

Factor $16$ out of $96$ .

$y = \frac{- 24 \pm \sqrt{16 (6) (- x + 1)}}{2 \cdot 3}$

Rewrite $16$ as $4^{2}$ .

$y = \frac{- 24 \pm \sqrt{4^{2} \cdot (6 (- x + 1))}}{2 \cdot 3}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{- 24 \pm \sqrt{{(2^{2})}^{2} \cdot (6 (- x + 1))}}{2 \cdot 3}$

Add parentheses.

$y = \frac{- 24 \pm \sqrt{{(2^{2})}^{2} \cdot (6 (- x + 1))}}{2 \cdot 3}$

Pull terms out from under the radical.

$y = \frac{- 24 \pm 2^{2} \sqrt{6 (- x + 1)}}{2 \cdot 3}$

Raise $2$ to the power of $2$ .

$y = \frac{- 24 \pm 4 \sqrt{6 (- x + 1)}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = \frac{- 24 \pm 4 \sqrt{6 (- x + 1)}}{6}$

Simplify $\frac{- 24 \pm 4 \sqrt{6 (- x + 1)}}{6}$ .

$y = \frac{- 12 \pm 2 \sqrt{6 (- x + 1)}}{3}$

Change the $\pm$ to $-$ .

$y = \frac{- 12 - 2 \sqrt{6 (- x + 1)}}{3}$

Factor $- 2$ out of $- 12 - 2 \sqrt{6 (- x + 1)}$ .

Factor $- 2$ out of $- 12$ .

$y = \frac{- 2 \cdot 6 - 2 \sqrt{6 (- x + 1)}}{3}$

Factor $- 2$ out of $- 2 \sqrt{6 (- x + 1)}$ .

$y = \frac{- 2 \cdot 6 - 2 \sqrt{6 (- x + 1)}}{3}$

Factor $- 2$ out of $- 2 (6) - 2 (\sqrt{6 (- x + 1)})$ .

$y = \frac{- 2 (6 + \sqrt{6 (- x + 1)})}{3}$

Move the negative in front of the fraction.

$y = - \frac{2 (6 + \sqrt{6 (- x + 1)})}{3}$

The final answer is the combination of both solutions.

$y = - \frac{2 (6 - \sqrt{6 (- x + 1)})}{3}$

$y = - \frac{2 (6 + \sqrt{6 (- x + 1)})}{3}$

$y = - \frac{2 (6 - \sqrt{6 (- x + 1)})}{3}$

$y = - \frac{2 (6 + \sqrt{6 (- x + 1)})}{3}$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Reorder terms.

$y = - (\frac{2}{3} \cdot (6 - \sqrt{6 (- x + 1)}))$

$y = - (\frac{2}{3} \cdot (6 + \sqrt{6 (- x + 1)}))$

Remove parentheses.

$y = - \frac{2}{3} \cdot (6 - \sqrt{6 (- x + 1)})$

$y = - (\frac{2}{3} \cdot (6 + \sqrt{6 (- x + 1)}))$

Remove parentheses.

$y = - \frac{2}{3} \cdot (6 - \sqrt{6 (- x + 1)})$

$y = - \frac{2}{3} \cdot (6 + \sqrt{6 (- x + 1)})$

Write in Standard Form 3y^2+8x+24y+40=0

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