The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.4181\\[1 em]x_2 &= 1.2674\\[1 em]x_3 &= -2.5159 \end{aligned} $$Polynomial $ 3x^3+5x^2-8x-4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.