Answer
$p\approx 1.830\qquad $or $p\approx-6.830$
Work Step by Step
$[1+\displaystyle \frac{2p}{5}]^{2}=3\qquad \color{blue}{\text{ ...take the square root from both sides } }$
$1+\displaystyle \frac{2p}{5}=\pm\sqrt{3} $
$\displaystyle \frac{5+2p}{5}=\pm\sqrt{3}\qquad \color{blue}{\text{ ... }/\times 5 }$
$5+2p=\pm 5\sqrt{3}\qquad \color{blue}{\text{ ... }/-5 }$
$2p=-5\pm\sqrt{3}\qquad \color{blue}{\text{ ... }/\div 2 }$
$p=\displaystyle \frac{-5\pm 5\sqrt{3}}{2}$
$p=\displaystyle \frac{-5+5\sqrt{3}}{2}\approx 1.830\qquad $or $p=\displaystyle \frac{-5-5\sqrt{3}}{2}\approx-6.830$
