Solving the cubic $ax^3+bx^2+cx+d=0$.

$\Delta =27 a^2 d^2-18 a b c d+4 a c^3+4 b^3 d-b^2 c^2$;     $\delta =\sqrt{\Delta }$;

$\Gamma =27 a^2 d-9 a b c+3 \sqrt{3} a \delta +2 b^3$;     $\gamma =\sqrt[3]{\frac{\Gamma }{2}}$;

$r=-\frac{(b^2-3 a c)/\gamma +b+\gamma }{3 a}$.