The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.646\\[1 em]x_2 &= -0.0103+1.6225i\\[1 em]x_3 &= -0.0103-1.6225i \end{aligned} $$Polynomial $ 3x^3+5x^2+8x+13 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.