The aim of this academic paper is to illustrate the thrilling history of polynomial equations in an unknown and their solutions. It will not only provide information about their exciting development, but also include the stories of the people who have been taking a closer look at the solution of these equations for centuries.This thesis is structured in such a way that the necessary mathematical tools and devices, which are essential for understanding the following chapters, are listed at the beginning. In order to not only examine the mere algebraic aspect of the theory of equations, also the numeric aspect is introduced in the third chapter. The reason for this is based on the fact that equations of a higher degree are increasingly difficult to solve with radicals. In some cases, it is not even possible and thus an alternative for the computation of roots needs to be offered. The further chapters exclusively focus on the possibility of solving equations in a mere algebraic way. For this, various tools are required, which will be examined and explained in chapter four. Chapters five and six deal with the sheer algebraic solvability of equations of degree one to n and the innovations which were revealed by the findings of equations of low- degree for the solution of equations of higher degrees.I also want to show which concepts of proof have been developed over the centuries. Many mathematicians have spent their entire lives on searching for characteristics and regularities to answer the questions arising from solving equations. For instance, in Greece, Egypt and Babylon, in the times before Christs birth, it was important to communicate and publish the results of and thoughts behind their research. During the Renaissance time, however, this was quite different: Mathematicians devoted themselves increasingly to the silent studies of equations.