Abel-Ruffini Theorem:

In 1823, using an incomplete proof written by Paolo Ruffini in 1799, Abel provided a proof of the impossibility of solving polynomial equations of degree 5 or higher, which take the form: ax^5+bx^4+cx^3+dx^2+ex+f=0

Most of us are quite familiar with the general solution to equations of degree 2 or lower, most commonly referred to as the quadratic equation. ax^2+bx+c=0.

Paolo Ruffini