Hi Roland,
It is a quintic equation, not quadratic, and in general there is no analytic or step-by-step solution. Using WL you can get a numerical solution:
eqn = 6 x^5 + 15 x^4 - 80 x^3 == -16;
Solve[eqn, x] // N
(* {{x -> -5.1121}, {x -> 0.615895}, {x -> 2.58957},
{x -> -0.296682 - 0.488923 I}, {x -> -0.296682 + 0.488923 I}} *)