The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2166\\[1 em]x_2 &= 0.9044\\[1 em]x_3 &= -1.5605+0.3428i\\[1 em]x_4 &= -1.5605-0.3428i \end{aligned} $$Polynomial $ 4x^4+8x^3-3x^2-9x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.