@cinebox it's nothing to do with quadrants! In a nutshell, if you study the types of numbers you can construct with +-*/ and nth roots, there's a connection to a certain mathematical "group". If you can solve a polynomial with +-*/ and nth roots, that translates to a certain group being "solvable", meaning having some smaller groups inside it. Then you can prove there are some groups which 1. Some quintic polynomials can be translated into, and 2. Aren't solvable.

The name of the type of math which the proof is using is "Galois theory".