The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.1737\\[1 em]x_2 &= -0.766\\[1 em]x_3 &= 0.9397 \end{aligned} $$Polynomial $ 8x^3-6x-1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.