Solve y^2-y-x=0

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

Solve for x

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

Steps for Solving Linear Equation

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

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

Add y to both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

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

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

Solve for y (complex solution)

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

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

Solve for y

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

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