Solve 12x^2-12y=z

$$12 x ^ { 2 } - 12 y = z$$

Solve for y

$$y=x^{2}-\frac{z}{12}$$

Steps for Solving Linear Equation

Subtract 12x^{2} from both sides.

$$-12y=z-12x^{2}$$

Divide both sides by -12.

$$\frac{-12y}{-12}=\frac{z-12x^{2}}{-12}$$

Dividing by -12 undoes the multiplication by -12.

$$y=\frac{z-12x^{2}}{-12}$$

Divide z-12x^{2} by -12.

$$y=x^{2}-\frac{z}{12}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3\left(12y+z\right)}}{6}$$

$$x=\frac{\sqrt{3\left(12y+z\right)}}{6}$$

Solve for x

$$x=\frac{\sqrt{3\left(12y+z\right)}}{6}$$

$$x=-\frac{\sqrt{3\left(12y+z\right)}}{6}\text{, }y\geq -\frac{z}{12}$$