minimum number of triangles in a simple graph

Question

I want to solve the following problem: If a simple graph on $n$ vertices has $m$ edges, then it has at least $\frac{m}{3n}(4m - n^2)$ triangles.

Can anyone suggest how to proceed?

Answer 1

You can find several solutions here https://artofproblemsolving.com/community/c6h78608p450334