One of the most basic questions in mathematics is finding
solutions to equations. In this post I want to make a short
overview of the ways to solve some of the common forms of
equations, and I also want to discus the history of how this
solutions were found. This is only the first post about this
subject, so it is mostly introductory. For the simplest
equations, the solutions are known for a long time, so I will
only mention since what period the solutions were known, and
will not discuss the ways they were developed. The most simple
equation is an equation of the form: The linear equations we now
how to solve. So, what other types of equations we have? The
next in line is the equation of the form: If we will take b=-1
we will have an even harder problem. The equation becomes then
x^2=-1. Until Gauss at the 18 century, such equations were
considered unsolvable. There are other, slightly more difficult
to solve, second degree polynomials. The most general form is:
We can now move b to the second site, and get