The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6885\\[1 em]x_2 &= -0.5243\\[1 em]x_3 &= -22.1642 \end{aligned} $$Polynomial $ x^3+22x^2-4x-8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.