Solve x^2-x-2y=0

$${ x }^{ 2 } -x-2y=0$$

Solve for y

$$y=\frac{x\left(x-1\right)}{2}$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add x to both sides.

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

The equation is in standard form.

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

Divide both sides by -2.

$$\frac{-2y}{-2}=\frac{x\left(1-x\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$y=\frac{x\left(1-x\right)}{-2}$$

Divide x\left(1-x\right) by -2.

$$y=-\frac{x\left(1-x\right)}{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{8y+1}+1}{2}$$

$$x=\frac{-\sqrt{8y+1}+1}{2}$$

Solve for x

$$x=\frac{\sqrt{8y+1}+1}{2}$$

$$x=\frac{-\sqrt{8y+1}+1}{2}\text{, }y\geq -\frac{1}{8}$$