Solve x^2+x-y+3=0

$${ x }^{ 2 } +x-y+3=0$$

Solve for y

$$y=x^{2}+x+3$$

Steps for Solving Linear Equation

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

$$x-y+3=-x^{2}$$

Subtract x from both sides.

$$-y+3=-x^{2}-x$$

Subtract 3 from both sides.

$$-y=-x^{2}-x-3$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{-x^{2}-x-3}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{-x^{2}-x-3}{-1}$$

Divide -x^{2}-x-3 by -1.

$$y=x^{2}+x+3$$

Solve for x (complex solution)

$$x=\frac{\sqrt{4y-11}-1}{2}$$

$$x=\frac{-\sqrt{4y-11}-1}{2}$$

Solve for x

$$x=\frac{\sqrt{4y-11}-1}{2}$$

$$x=\frac{-\sqrt{4y-11}-1}{2}\text{, }y\geq \frac{11}{4}$$