The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8359\\[1 em]x_2 &= 0.4179+0.5234i\\[1 em]x_3 &= 0.4179-0.5234i \end{aligned} $$Polynomial $ -8x^3+2x-3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.