The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.3495\\[1 em]x_2 &= 0.1748+0.736i\\[1 em]x_3 &= 0.1748-0.736i \end{aligned} $$Polynomial $ 40x^3+18x+8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.