The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.6437\\[1 em]x_2 &= -1.1188\\[1 em]x_3 &= 1.4613\\[1 em]x_4 &= 3.8011 \end{aligned} $$Polynomial $ 2x^4-7x^3-6x^2+12x+8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.