Page "Algebraic solution" Paragraph 6

There exist more complicated algebraic solutions for the general cubic equation and quartic equation.

The Abel-Ruffini theorem states that the general quintic equation lacks an algebraic solution, and this directly implies that the general polynomial equation of degree n, for n ≥ 5, cannot be solved algebraically.

However, under certain conditions algebraic solutions can be obtained ; for example, the equation can be solved as