The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.4543+1.8682i\\[1 em]x_2 &= 1.4543-1.8682i\\[1 em]x_3 &= -1.4543+0.86i\\[1 em]x_4 &= -1.4543-0.86i \end{aligned} $$Polynomial $ x^4+8x+16 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.