Solve a^2+3a-p=0

$$a ^ { 2 } + 3 a - p = 0$$

Solve for p

$$p=a\left(a+3\right)$$

Steps for Solving Linear Equation

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

$$3a-p=-a^{2}$$

Subtract 3a from both sides.

$$-p=-a^{2}-3a$$

Divide both sides by -1.

$$\frac{-p}{-1}=-\frac{a\left(a+3\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$p=-\frac{a\left(a+3\right)}{-1}$$

Divide -a\left(3+a\right) by -1.

$$p=a\left(a+3\right)$$

Solve for a (complex solution)

$$a=\frac{\sqrt{4p+9}-3}{2}$$

$$a=\frac{-\sqrt{4p+9}-3}{2}$$

Solve for a

$$a=\frac{\sqrt{4p+9}-3}{2}$$

$$a=\frac{-\sqrt{4p+9}-3}{2}\text{, }p\geq -\frac{9}{4}$$