Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been given to solving the master students in mathematics, many years. Unfortunately, none of them were able to give its solution. Therefore, we proposed the drafting of this paper.