The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \frac{ 2 \sqrt{ 6}}{ 3 }\\[1 em]x_2 &= -2 \frac{\sqrt{ 6 }}{ 3 } \end{aligned} $$The solutions of $ 3x^2-8 = 0 $ are: $ x = -2 \dfrac{\sqrt{ 6 }}{ 3 } ~ \text{and} ~ x = \dfrac{ 2 \sqrt{ 6}}{ 3 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.