Solve x+x^2-y=0

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

Solve for y

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

Steps for Solving Linear Equation

Subtract x from both sides. Anything subtracted from zero gives its negation.

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

Subtract x^{2} from both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

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