The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -3.7112\\[1 em]x_2 &= -0.1444+2.4305i\\[1 em]x_3 &= -0.1444-2.4305i \end{aligned} $$Polynomial $ x^3+4x^2+7x+22 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.