The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.3709+0.6485i\\[1 em]x_2 &= 1.3709-0.6485i\\[1 em]x_3 &= -1.3709+1.8271i\\[1 em]x_4 &= -1.3709-1.8271i \end{aligned} $$Polynomial $ x^4-8x+12 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.