Answer
$p=24$ or $x=\frac{3}{2}$
Work Step by Step
$ 51p=2p^{2}+72\qquad$...add $(-2p^{2}-72)$ to both sides.
$ 51p-2p^{2}-72=2p^{2}+72-2p^{2}-72\qquad$...add like terms.
$-2p^{2}+51p-72=0\qquad$...mulitiply both sides by $-1$.
$ 2p^{2}-51p+72=0\qquad$... solve with the Quadractic formula. $a=2,\ b=-51,\ c=72$
$ p=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\qquad$... substitute $b$ for $-51,\ a$ for $2$ and $c$ for $72$.
$ p=\displaystyle \frac{-(-51)\pm\sqrt{(-51)^{2}-4\cdot(72)\cdot 2}}{2\cdot 2}\qquad$... simplify.
$p=\displaystyle \frac{51\pm\sqrt{2601-576}}{4}$
$p=\displaystyle \frac{51\pm\sqrt{2025}}{4}$
$ p=\displaystyle \frac{51\pm 45}{4}\qquad$... the symbol $\pm$ indicates two solutions.
$p=\displaystyle \frac{51+45}{4}=\frac{96}{4}=24$ or $x=\displaystyle \frac{51-45}{4}=\frac{6}{4}=\frac{3}{2}$
