The study of algebraic equations is a subject of great importance for mathematics, because they are essential for the essential pillars of Algebra, such as its fundamental theorem, which establishes that: “every polynomial of degree greater than zero has a root. The domain of the variable is the set of complex numbers, which is an extension of the real numbers”. This concept of calculating roots to polynomials has generated various techniques to calculate the solution of algebraic equations, which has contributed to making great contributions to mathematics and geometry. This work presents the analysis and development of algebraic equations from Egyptian culture to the current era. It is important to highlight that at present the solution of algebraic equations is being studied by mathematicians and professionals from other careers, due to its application in solving mathematical problems as well as those of other sciences.