Answer
$p=2\pm\dfrac{\sqrt{30}}{3}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
3p^2-12p+2=0\\
p^2-4p+\dfrac{2}{3}=0\\
p^2-4p=-\dfrac{2}{3}\\
p^2-4p+\left( \dfrac{-4}{2} \right)^2=-\dfrac{2}{3}+\left( \dfrac{-4}{2}\right)^2\\
p^2-4p+4=-\dfrac{2}{3}+4\\
\left( p-2 \right)^2=\dfrac{10}{3}\\
p-2=\pm\sqrt{\dfrac{10}{3}}\\
p=2\pm\sqrt{\dfrac{10}{3}}\\
p=2\pm\dfrac{\sqrt{30}}{3}
.\end{array}
