Solve for y 2x-y^2=7

$2 x - y^{2} = 7$

Subtract $2 x$ from both sides of the equation.

$- y^{2} = 7 - 2 x$

Divide each term in $- y^{2} = 7 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y^{2} = 7 - 2 x$ by $- 1$ .

$\frac{- y^{2}}{- 1} = \frac{7}{- 1} + \frac{- 2 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y^{2}}{1} = \frac{7}{- 1} + \frac{- 2 x}{- 1}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{7}{- 1} + \frac{- 2 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $7$ by $- 1$ .

$y^{2} = - 7 + \frac{- 2 x}{- 1}$

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y^{2} = - 7 - 1 \cdot (- 2 x)$

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y^{2} = - 7 - (- 2 x)$

Multiply $- 2$ by $- 1$ .

$y^{2} = - 7 + 2 x$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{- 7 + 2 x}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{- 7 + 2 x}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{- 7 + 2 x}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{- 7 + 2 x}$

$y = - \sqrt{- 7 + 2 x}$

$y = \sqrt{- 7 + 2 x}$

$y = - \sqrt{- 7 + 2 x}$