Scanned pages from the famous article Sur la Résolution du L'Équation du Cinquième Degré by Charles Hermite, comptes rendus de l'Académie des Science, t. XLVI, 1858 (I), p.508. In this article, Hermite presents a solution of the 5th degree polynomial. Eric Temple Bell in his famous book Men of Mathematics describes it like this:

(page 509) In short order Hermite then proceeds to solve the general equation of the fifth degree, using for the purpose, elliptic functions (strictly, elliptic modular functions, but the distinction is of no importance here). It is almost impossible to convey to a non-mathematician the spectacular brilliance of such a feat; to give a very inadequate simile, Hermite found the famous 'lost chord' where no mortal had the slightest suspicion that such an elusive thing existed anywhere in time and space. Needless to say his totally unforeseen success created a sensation in the mathematical world. Better, it inaugurated a new department of algebra and analysis in which the grand problem is to discover and investigate those functions in terms of which the general equation of the nth degree can be solved explicitly in finite form. The best result so far obtained is that of Hermite's pupil, Poincaré (in the 1880s), who created the functions giving the required solution. These turned out to be a natural generalization of the elliptic functions.