The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5344\\[1 em]x_2 &= -2.2328+0.7926i\\[1 em]x_3 &= -2.2328-0.7926i \end{aligned} $$Polynomial $ x^3+5x^2+8x+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.