The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7211\\[1 em]x_2 &= 0.3606+0.6245i\\[1 em]x_3 &= 0.3606-0.6245i \end{aligned} $$Polynomial $ -8x^3-3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.