The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2735\\[1 em]x_2 &= -0.5432\\[1 em]x_3 &= -6.7303 \end{aligned} $$Polynomial $ 3x^3+21x^2+5x-3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.