TITLE: Formula for quadratic equations from Galois theory
QUESTION [7 upvotes]: Can we deduce the classical formula for the solutions of a quadratic equations $ax^2+bx+c=0$ using Galois theory?

REPLY [2 votes]: An alternative way of deriving the quadratic formula is via the method of Lagrange resolvents, which is an early part of Galois theory (see here, under 
Lagrange resolvents).