Quintic Equation 

where a , b , c , d , e and f are members of a field , typically the rational numbers , the real numbers or the complex numbers , and a is nonzero. In other words, a quintic function is defined by a polynomial of degree five.

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions , subtractions , multiplications , divisions , and root extractions , as rigorously demonstrated by Abel ( Abel's impossibility theorem ) and Galois. However, certain classes of quintic equations can be solved in this manner.