> (almost) the entire work of Diophantus, the man diophantine equations are named after, is basically obsoleted by \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

This is nowhere close to an accurate statement, even if we only consider works that have survived to the present (most of his work has been lost). Have you tried to read the work of Diophantus or any modern summary?