Solve 3p^2+7a-28=(a+6)

$$3 p ^ { 2 } + 7 a - 28 = ( a + 6 )$$

Solve for a

$$a=-\frac{p^{2}}{2}+\frac{17}{3}$$

Steps for Solving Linear Equation

Subtract a from both sides.

$$3p^{2}+7a-28-a=6$$

Combine 7a and -a to get 6a.

$$3p^{2}+6a-28=6$$

Subtract 3p^{2} from both sides.

$$6a-28=6-3p^{2}$$

Add 28 to both sides.

$$6a=6-3p^{2}+28$$

Add 6 and 28 to get 34.

$$6a=34-3p^{2}$$

Divide both sides by 6.

$$\frac{6a}{6}=\frac{34-3p^{2}}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$a=\frac{34-3p^{2}}{6}$$

Divide 34-3p^{2} by 6.

$$a=-\frac{p^{2}}{2}+\frac{17}{3}$$

Solve for p (complex solution)

$$p=-\frac{\sqrt{102-18a}}{3}$$

$$p=\frac{\sqrt{102-18a}}{3}$$

Solve for p

$$p=\frac{\sqrt{102-18a}}{3}$$

$$p=-\frac{\sqrt{102-18a}}{3}\text{, }a\leq \frac{17}{3}$$