Solve 3x^2-y-23=y-7

$$3 x ^ { 2 } - y - 23 = y - 7$$

Solve for y

$$y=\frac{3x^{2}}{2}-8$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$3x^{2}-y-23-y=-7$$

Combine -y and -y to get -2y.

$$3x^{2}-2y-23=-7$$

Subtract 3x^{2} from both sides.

$$-2y-23=-7-3x^{2}$$

Add 23 to both sides.

$$-2y=-7-3x^{2}+23$$

Add -7 and 23 to get 16.

$$-2y=16-3x^{2}$$

Divide both sides by -2.

$$\frac{-2y}{-2}=\frac{16-3x^{2}}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$y=\frac{16-3x^{2}}{-2}$$

Divide 16-3x^{2} by -2.

$$y=\frac{3x^{2}}{2}-8$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6\left(y+8\right)}}{3}$$

$$x=\frac{\sqrt{6\left(y+8\right)}}{3}$$

Solve for x

$$x=\frac{\sqrt{6\left(y+8\right)}}{3}$$

$$x=-\frac{\sqrt{6\left(y+8\right)}}{3}\text{, }y\geq -8$$