Solve a^2+a-b=0

$$a ^ { 2 } + a - b = 0$$

Solve for b

$$b=a\left(a+1\right)$$

Steps for Solving Linear Equation

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

$$a-b=-a^{2}$$

Subtract a from both sides.

$$-b=-a^{2}-a$$

Divide both sides by -1.

$$\frac{-b}{-1}=-\frac{a\left(a+1\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=-\frac{a\left(a+1\right)}{-1}$$

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

$$b=a\left(a+1\right)$$

Solve for a

$$a=\frac{\sqrt{4b+1}-1}{2}$$

$$a=\frac{-\sqrt{4b+1}-1}{2}\text{, }b\geq -\frac{1}{4}$$