Write in Standard Form y^2+6x-4y-9=0

$y^{2} + 6 x - 4 y - 9 = 0$

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 $a = 1$ , $b = - 4$ , and $c = 6 x - 9$ into the quadratic formula and solve for $y$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (1 \cdot (6 x - 9))}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Factor $- 4$ out of ${(- 4)}^{2} - 4 \cdot 1 \cdot (6 x - 9)$ .

Factor $- 4$ out of ${(- 4)}^{2}$ .

$y = \frac{4 \pm \sqrt{- 4 \cdot - 4 - 4 \cdot 1 \cdot (6 x - 9)}}{2 \cdot 1}$

Factor $- 4$ out of $- 4 \cdot 1 \cdot (6 x - 9)$ .

$y = \frac{4 \pm \sqrt{- 4 \cdot - 4 - 4 (1 \cdot (6 x - 9))}}{2 \cdot 1}$

Factor $- 4$ out of $- 4 \cdot - 4 - 4 (1 \cdot (6 x - 9))$ .

$y = \frac{4 \pm \sqrt{- 4 (- 4 + 1 \cdot (6 x - 9))}}{2 \cdot 1}$

Multiply $6 x - 9$ by $1$ .

$y = \frac{4 \pm \sqrt{- 4 (- 4 + 6 x - 9)}}{2 \cdot 1}$

Subtract $9$ from $- 4$ .

$y = \frac{4 \pm \sqrt{- 4 (6 x - 13)}}{2 \cdot 1}$

Rewrite $- 4 (6 x - 13)$ as $2^{2} \cdot (- 1 (6 x - 13))$ .

Factor $4$ out of $- 4$ .

$y = \frac{4 \pm \sqrt{4 (- 1) (6 x - 13)}}{2 \cdot 1}$

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

$y = \frac{4 \pm \sqrt{2^{2} \cdot (- 1 (6 x - 13))}}{2 \cdot 1}$

Add parentheses.

$y = \frac{4 \pm \sqrt{2^{2} \cdot (- 1 (6 x - 13))}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{4 \pm 2 \sqrt{- 1 (6 x - 13)}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{4 \pm 2 \sqrt{- 1 (6 x - 13)}}{2}$

Simplify $\frac{4 \pm 2 \sqrt{- 1 (6 x - 13)}}{2}$ .

$y = 2 \pm \sqrt{- 1 (6 x - 13)}$

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

Simplify the numerator.

Factor $- 4$ out of ${(- 4)}^{2} - 4 \cdot 1 \cdot (6 x - 9)$ .

Factor $- 4$ out of ${(- 4)}^{2}$ .

$y = \frac{4 \pm \sqrt{- 4 \cdot - 4 - 4 \cdot 1 \cdot (6 x - 9)}}{2 \cdot 1}$

Factor $- 4$ out of $- 4 \cdot 1 \cdot (6 x - 9)$ .

$y = \frac{4 \pm \sqrt{- 4 \cdot - 4 - 4 (1 \cdot (6 x - 9))}}{2 \cdot 1}$

Factor $- 4$ out of $- 4 \cdot - 4 - 4 (1 \cdot (6 x - 9))$ .

$y = \frac{4 \pm \sqrt{- 4 (- 4 + 1 \cdot (6 x - 9))}}{2 \cdot 1}$

Multiply $6 x - 9$ by $1$ .

$y = \frac{4 \pm \sqrt{- 4 (- 4 + 6 x - 9)}}{2 \cdot 1}$

Subtract $9$ from $- 4$ .

$y = \frac{4 \pm \sqrt{- 4 (6 x - 13)}}{2 \cdot 1}$

Rewrite $- 4 (6 x - 13)$ as $2^{2} \cdot (- 1 (6 x - 13))$ .

Factor $4$ out of $- 4$ .

$y = \frac{4 \pm \sqrt{4 (- 1) (6 x - 13)}}{2 \cdot 1}$

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

$y = \frac{4 \pm \sqrt{2^{2} \cdot (- 1 (6 x - 13))}}{2 \cdot 1}$

Add parentheses.

$y = \frac{4 \pm \sqrt{2^{2} \cdot (- 1 (6 x - 13))}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{4 \pm 2 \sqrt{- 1 (6 x - 13)}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{4 \pm 2 \sqrt{- 1 (6 x - 13)}}{2}$

Simplify $\frac{4 \pm 2 \sqrt{- 1 (6 x - 13)}}{2}$ .

$y = 2 \pm \sqrt{- 1 (6 x - 13)}$

Change the $\pm$ to $+$ .

$y = 2 + \sqrt{- 1 (6 x - 13)}$

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

Simplify the numerator.

Factor $- 4$ out of ${(- 4)}^{2} - 4 \cdot 1 \cdot (6 x - 9)$ .

Factor $- 4$ out of ${(- 4)}^{2}$ .

$y = \frac{4 \pm \sqrt{- 4 \cdot - 4 - 4 \cdot 1 \cdot (6 x - 9)}}{2 \cdot 1}$

Factor $- 4$ out of $- 4 \cdot 1 \cdot (6 x - 9)$ .

$y = \frac{4 \pm \sqrt{- 4 \cdot - 4 - 4 (1 \cdot (6 x - 9))}}{2 \cdot 1}$

Factor $- 4$ out of $- 4 \cdot - 4 - 4 (1 \cdot (6 x - 9))$ .

$y = \frac{4 \pm \sqrt{- 4 (- 4 + 1 \cdot (6 x - 9))}}{2 \cdot 1}$

Multiply $6 x - 9$ by $1$ .

$y = \frac{4 \pm \sqrt{- 4 (- 4 + 6 x - 9)}}{2 \cdot 1}$

Subtract $9$ from $- 4$ .

$y = \frac{4 \pm \sqrt{- 4 (6 x - 13)}}{2 \cdot 1}$

Rewrite $- 4 (6 x - 13)$ as $2^{2} \cdot (- 1 (6 x - 13))$ .

Factor $4$ out of $- 4$ .

$y = \frac{4 \pm \sqrt{4 (- 1) (6 x - 13)}}{2 \cdot 1}$

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

$y = \frac{4 \pm \sqrt{2^{2} \cdot (- 1 (6 x - 13))}}{2 \cdot 1}$

Add parentheses.

$y = \frac{4 \pm \sqrt{2^{2} \cdot (- 1 (6 x - 13))}}{2 \cdot 1}$

Pull terms out from under the radical.

$y = \frac{4 \pm 2 \sqrt{- 1 (6 x - 13)}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{4 \pm 2 \sqrt{- 1 (6 x - 13)}}{2}$

Simplify $\frac{4 \pm 2 \sqrt{- 1 (6 x - 13)}}{2}$ .

$y = 2 \pm \sqrt{- 1 (6 x - 13)}$

Change the $\pm$ to $-$ .

$y = 2 - \sqrt{- 1 (6 x - 13)}$

The final answer is the combination of both solutions.

$y = 2 + \sqrt{- 1 (6 x - 13)}$

$y = 2 - \sqrt{- 1 (6 x - 13)}$

$y = 2 + \sqrt{- 1 (6 x - 13)}$

$y = 2 - \sqrt{- 1 (6 x - 13)}$

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

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

Rewrite $- 1 (6 x - 13)$ as $- (6 x - 13)$ .

$y = 2 + \sqrt{- (6 x - 13)}$

$y = 2 - \sqrt{- (6 x - 13)}$

Write in Standard Form y^2+6x-4y-9=0

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