The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.4665\\[1 em]x_2 &= 3.5552\\[1 em]x_3 &= 4.4113 \end{aligned} $$Polynomial $ 2x^3-13x^2+8x+46 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.