It is my first post here.
I'm studying Group Theory and I found lots of examples of it but for advanced applications.
What I'm trying to find or understand is just the opposit! I want to use Group Theory to solve quadratic polynomials, for example. Can someone please provide some link or example of how to apply Group Theory to solve simple things like to find the roots of a polynomial of degree $n \leq 4$ ? A simple: $x^2+x+c=0$ would be enough to let me start to use it in GAP and Sage Package.
Thank you in advance.