The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.6757\\[1 em]x_2 &= -3.5091\\[1 em]x_3 &= -0.5833+1.8442i\\[1 em]x_4 &= -0.5833-1.8442i \end{aligned} $$Polynomial $ x^4+3x^3-22 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.