Timeline for Solution to sixth order equation

6 events

when toggle format	what		by	license	comment
Dec 13, 2021 at 11:08	comment	added	Johannes Trost		Note that $108^{2}=11664$. By introducing $\xi:=108 x$ the solution's formula becomes rather compact.
Dec 13, 2021 at 1:12	comment	added	Alexandre Eremenko		Since the RHS is strictly increasing, zero at zero and tends to infinity, existence and uniqueness of a positive solution is evident.
Dec 12, 2021 at 20:24	history	edited	Carlo Beenakker	CC BY-SA 4.0	added 6 characters in body
Dec 12, 2021 at 18:58	comment	added	Saúl RM		To give an idea of how you can come up with this, you can realize that substituting $z=y+\frac{1}{2}$, you obtain $x$ as an even function of $z$ (a way to suspect this is noticing that the roots of the given degree 6 polynomial are symmetric respect to $-\frac{1}{2}$), so you can call another variable $t=z^2$ and then you have $x$ as a cubic polynomial in $t$, which allows you to use Cardano´s formula for the cubic equation.
Dec 12, 2021 at 18:44	vote	accept	Benjamin L. Warren
Dec 12, 2021 at 18:43	history	answered	Carlo Beenakker	CC BY-SA 4.0