A formula to solve sextic degree equation

Abstract

According to the Abel-Ruffini theorem, equations of degree equal to or greater than 5 cannot, in most cases, be solved by radicals. Due of this theorem we will present a formula that solves specific cases of sixth degree equations using Martinellis polynomial as a base. To better understand how this formula works, we will solve a sixth degree equation as an example. We will also see that all sixth degree equations that meet the coefficient criterion have a resolvent of fifth degree that can be splitted into a second degree and a third degree equation. Throughout the paper we will see a demonstration of the ratio of the coefficients of a sixth degree equation that can be solved with the formula that will be presented this paper