Solve x^2+x=5-y

$${ x }^{ 2 } +x=5-y$$

Solve for y

$$y=5-x-x^{2}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$5-y=x^{2}+x$$

Subtract 5 from both sides.

$$-y=x^{2}+x-5$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{x^{2}+x-5}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{x^{2}+x-5}{-1}$$

Divide x^{2}+x-5 by -1.

$$y=5-x-x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{21-4y}-1}{2}$$

$$x=\frac{-\sqrt{21-4y}-1}{2}$$

Solve for x

$$x=\frac{\sqrt{21-4y}-1}{2}$$

$$x=\frac{-\sqrt{21-4y}-1}{2}\text{, }y\leq \frac{21}{4}$$