The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.9196\\[1 em]x_2 &= 2.4598+0.6882i\\[1 em]x_3 &= 2.4598-0.6882i \end{aligned} $$Polynomial $ x^3-4x^2+2x+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.