The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.9316\\[1 em]x_2 &= 2.6768\\[1 em]x_3 &= 4.2548 \end{aligned} $$Polynomial $ -x^3+5x^2+2x-22 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.