Solve x^2-x-y=0

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

Solve for y

$$y=x\left(x-1\right)$$

Steps for Solving Linear Equation

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

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

Add x to both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

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

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

Solve for x (complex solution)

$$x=\frac{\sqrt{4y+1}+1}{2}$$

$$x=\frac{-\sqrt{4y+1}+1}{2}$$

Solve for x

$$x=\frac{\sqrt{4y+1}+1}{2}$$

$$x=\frac{-\sqrt{4y+1}+1}{2}\text{, }y\geq -\frac{1}{4}$$