Editing Quintic function (section)

===Solving with Bring radicals===
{{Main article|Bring radical}}

A [[Tschirnhaus transformation]], which may be computed by solving a [[quartic equation]], reduces the general quintic equation of the form 
:<math>x^5 + a_4x^4 + a_3x^3 + a_2x^2 + a_1x + a_0 = 0\,</math> 
to the [[Bring–Jerrard normal form]] {{math|''x''<sup>5</sup> − ''x'' + ''t'' {{=}} 0}}.

The roots of this equation cannot be expressed by radicals. However, in 1858, [[Charles Hermite]] published the first known solution of this equation in terms of [[elliptic function]]s.<ref name="hermite">{{cite journal
 | last = Hermite
 | first = Charles
 | year = 1858
 | title =  Sur la résolution de l'équation du cinquième degré 
 | journal = Comptes Rendus de l'Académie des Sciences
 | volume = XLVI
 | issue = I
 | pages = 508–515}}</ref>
At around the same time [[Francesco Brioschi]]<ref>
{{cite journal
 | last = Brioschi
 | first = Francesco
 | year = 1858
 | title =  Sul Metodo di Kronecker per la Risoluzione delle Equazioni di Quinto Grado 
 | journal = Atti Dell'i. R. Istituto Lombardo di Scienze, Lettere ed Arti
 | volume = I
 | pages = 275–282}}</ref> 
and [[Leopold Kronecker]]<ref>
{{cite journal
 | last = Kronecker
 | first = Leopold
 | year = 1858
 | title =  Sur la résolution de l'equation du cinquième degré, extrait d'une lettre adressée à M. Hermite 
 | journal = Comptes Rendus de l'Académie des Sciences
 | volume = XLVI
 | issue = I
 | pages = 1150–1152}}</ref>
came upon equivalent solutions.

See [[Bring radical]] for details on these solutions and some related ones.