Write in Standard Form x+3y^2+12y=18

$x + 3 y^{2} + 12 y = 18$

Solve for $y$ .

Subtract $18$ from both sides of the equation.

$x + 3 y^{2} + 12 y - 18 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 3$ , $b = 12$ , and $c = x - 18$ into the quadratic formula and solve for $y$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (3 \cdot (x - 18))}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$y = \frac{- 12 \pm \sqrt{144 - 4 \cdot 3 \cdot (x - 18)}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$y = \frac{- 12 \pm \sqrt{144 - 12 \cdot (x - 18)}}{2 \cdot 3}$

Apply the distributive property.

$y = \frac{- 12 \pm \sqrt{144 - 12 x - 12 \cdot - 18}}{2 \cdot 3}$

Multiply $- 12$ by $- 18$ .

$y = \frac{- 12 \pm \sqrt{144 - 12 x + 216}}{2 \cdot 3}$

Add $144$ and $216$ .

$y = \frac{- 12 \pm \sqrt{- 12 x + 360}}{2 \cdot 3}$

Factor $12$ out of $- 12 x + 360$ .

Factor $12$ out of $- 12 x$ .

$y = \frac{- 12 \pm \sqrt{12 (- x) + 360}}{2 \cdot 3}$

Factor $12$ out of $360$ .

$y = \frac{- 12 \pm \sqrt{12 (- x) + 12 (30)}}{2 \cdot 3}$

Factor $12$ out of $12 (- x) + 12 (30)$ .

$y = \frac{- 12 \pm \sqrt{12 (- x + 30)}}{2 \cdot 3}$

Rewrite $12 (- x + 30)$ as $2^{2} \cdot (3 (- x + 30))$ .

Factor $4$ out of $12$ .

$y = \frac{- 12 \pm \sqrt{4 (3) (- x + 30)}}{2 \cdot 3}$

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

$y = \frac{- 12 \pm \sqrt{2^{2} \cdot (3 (- x + 30))}}{2 \cdot 3}$

Add parentheses.

$y = \frac{- 12 \pm \sqrt{2^{2} \cdot (3 (- x + 30))}}{2 \cdot 3}$

Pull terms out from under the radical.

$y = \frac{- 12 \pm 2 \sqrt{3 (- x + 30)}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = \frac{- 12 \pm 2 \sqrt{3 (- x + 30)}}{6}$

Simplify $\frac{- 12 \pm 2 \sqrt{3 (- x + 30)}}{6}$ .

$y = \frac{- 6 \pm \sqrt{3 (- x + 30)}}{3}$

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

Simplify the numerator.

Raise $12$ to the power of $2$ .

$y = \frac{- 12 \pm \sqrt{144 - 4 \cdot 3 \cdot (x - 18)}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$y = \frac{- 12 \pm \sqrt{144 - 12 \cdot (x - 18)}}{2 \cdot 3}$

Apply the distributive property.

$y = \frac{- 12 \pm \sqrt{144 - 12 x - 12 \cdot - 18}}{2 \cdot 3}$

Multiply $- 12$ by $- 18$ .

$y = \frac{- 12 \pm \sqrt{144 - 12 x + 216}}{2 \cdot 3}$

Add $144$ and $216$ .

$y = \frac{- 12 \pm \sqrt{- 12 x + 360}}{2 \cdot 3}$

Factor $12$ out of $- 12 x + 360$ .

Factor $12$ out of $- 12 x$ .

$y = \frac{- 12 \pm \sqrt{12 (- x) + 360}}{2 \cdot 3}$

Factor $12$ out of $360$ .

$y = \frac{- 12 \pm \sqrt{12 (- x) + 12 (30)}}{2 \cdot 3}$

Factor $12$ out of $12 (- x) + 12 (30)$ .

$y = \frac{- 12 \pm \sqrt{12 (- x + 30)}}{2 \cdot 3}$

Rewrite $12 (- x + 30)$ as $2^{2} \cdot (3 (- x + 30))$ .

Factor $4$ out of $12$ .

$y = \frac{- 12 \pm \sqrt{4 (3) (- x + 30)}}{2 \cdot 3}$

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

$y = \frac{- 12 \pm \sqrt{2^{2} \cdot (3 (- x + 30))}}{2 \cdot 3}$

Add parentheses.

$y = \frac{- 12 \pm \sqrt{2^{2} \cdot (3 (- x + 30))}}{2 \cdot 3}$

Pull terms out from under the radical.

$y = \frac{- 12 \pm 2 \sqrt{3 (- x + 30)}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = \frac{- 12 \pm 2 \sqrt{3 (- x + 30)}}{6}$

Simplify $\frac{- 12 \pm 2 \sqrt{3 (- x + 30)}}{6}$ .

$y = \frac{- 6 \pm \sqrt{3 (- x + 30)}}{3}$

Change the $\pm$ to $+$ .

$y = \frac{- 6 + \sqrt{3 (- x + 30)}}{3}$

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

$y = \frac{- 1 \cdot 6 + \sqrt{3 (- x + 30)}}{3}$

Factor $- 1$ out of $\sqrt{3 (- x + 30)}$ .

$y = \frac{- 1 \cdot 6 - 1 (- \sqrt{3 (- x + 30)})}{3}$

Factor $- 1$ out of $- 1 (6) - 1 (- \sqrt{3 (- x + 30)})$ .

$y = \frac{- 1 (6 - \sqrt{3 (- x + 30)})}{3}$

Move the negative in front of the fraction.

$y = - \frac{6 - \sqrt{3 (- x + 30)}}{3}$

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

Simplify the numerator.

Raise $12$ to the power of $2$ .

$y = \frac{- 12 \pm \sqrt{144 - 4 \cdot 3 \cdot (x - 18)}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$y = \frac{- 12 \pm \sqrt{144 - 12 \cdot (x - 18)}}{2 \cdot 3}$

Apply the distributive property.

$y = \frac{- 12 \pm \sqrt{144 - 12 x - 12 \cdot - 18}}{2 \cdot 3}$

Multiply $- 12$ by $- 18$ .

$y = \frac{- 12 \pm \sqrt{144 - 12 x + 216}}{2 \cdot 3}$

Add $144$ and $216$ .

$y = \frac{- 12 \pm \sqrt{- 12 x + 360}}{2 \cdot 3}$

Factor $12$ out of $- 12 x + 360$ .

Factor $12$ out of $- 12 x$ .

$y = \frac{- 12 \pm \sqrt{12 (- x) + 360}}{2 \cdot 3}$

Factor $12$ out of $360$ .

$y = \frac{- 12 \pm \sqrt{12 (- x) + 12 (30)}}{2 \cdot 3}$

Factor $12$ out of $12 (- x) + 12 (30)$ .

$y = \frac{- 12 \pm \sqrt{12 (- x + 30)}}{2 \cdot 3}$

Rewrite $12 (- x + 30)$ as $2^{2} \cdot (3 (- x + 30))$ .

Factor $4$ out of $12$ .

$y = \frac{- 12 \pm \sqrt{4 (3) (- x + 30)}}{2 \cdot 3}$

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

$y = \frac{- 12 \pm \sqrt{2^{2} \cdot (3 (- x + 30))}}{2 \cdot 3}$

Add parentheses.

$y = \frac{- 12 \pm \sqrt{2^{2} \cdot (3 (- x + 30))}}{2 \cdot 3}$

Pull terms out from under the radical.

$y = \frac{- 12 \pm 2 \sqrt{3 (- x + 30)}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = \frac{- 12 \pm 2 \sqrt{3 (- x + 30)}}{6}$

Simplify $\frac{- 12 \pm 2 \sqrt{3 (- x + 30)}}{6}$ .

$y = \frac{- 6 \pm \sqrt{3 (- x + 30)}}{3}$

Change the $\pm$ to $-$ .

$y = \frac{- 6 - \sqrt{3 (- x + 30)}}{3}$

Factor $- 1$ out of $- 6 - \sqrt{3 (- x + 30)}$ .

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

$y = \frac{- 1 \cdot 6 - \sqrt{3 (- x + 30)}}{3}$

Factor $- 1$ out of $- \sqrt{3 (- x + 30)}$ .

$y = \frac{- 1 \cdot 6 - (\sqrt{3 (- x + 30)})}{3}$

Factor $- 1$ out of $- 1 (6) - (\sqrt{3 (- x + 30)})$ .

$y = \frac{- 1 (6 + \sqrt{3 (- x + 30)})}{3}$

Rewrite $- 1 (6 + \sqrt{3 (- x + 30)})$ as $- (6 + \sqrt{3 (- x + 30)})$ .

$y = \frac{- (6 + \sqrt{3 (- x + 30)})}{3}$

Move the negative in front of the fraction.