The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8486+0.9693i\\[1 em]x_2 &= 0.8486-0.9693i\\[1 em]x_3 &= -1.8486+0.4449i\\[1 em]x_4 &= -1.8486-0.4449i \end{aligned} $$Polynomial $ x^4+2x^3-x^2+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.