Solve 2x-y^2=4y+10

$$2 x - y ^ { 2 } = 4 y + 10$$

Solve for x

$$x=\frac{y^{2}+4y+10}{2}$$

Steps for Solving Linear Equation

Add y^{2} to both sides.

$$2x=4y+10+y^{2}$$

The equation is in standard form.

$$2x=y^{2}+4y+10$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{y^{2}+4y+10}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{y^{2}+4y+10}{2}$$

Divide 4y+10+y^{2} by 2.

$$x=\frac{y^{2}}{2}+2y+5$$

Solve for y (complex solution)

$$y=-\sqrt{2\left(x-3\right)}-2$$

$$y=\sqrt{2\left(x-3\right)}-2$$

Solve for y

$$y=-\sqrt{2\left(x-3\right)}-2$$

$$y=\sqrt{2\left(x-3\right)}-2\text{, }x\geq 3$$