The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.2174\\[1 em]x_2 &= 0.6087+0.9282i\\[1 em]x_3 &= 0.6087-0.9282i \end{aligned} $$Polynomial $ 4x^3-x+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.