The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2731\\[1 em]x_2 &= 3.5422\\[1 em]x_3 &= -8.2691 \end{aligned} $$Polynomial $ x^3+5x^2-28x-8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.