The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 2.31\\[1 em]x_2 &= -1.7505\\[1 em]x_3 &= 5.4406 \end{aligned} $$Polynomial $ x^3-6x^2-x+22 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.