The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7709\\[1 em]x_2 &= 0.3855+1.5639i\\[1 em]x_3 &= 0.3855-1.5639i \end{aligned} $$Polynomial $ x^3+2x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.