I have this equation, and I want to find solution for x.
$\begin{align*}&(-2 x+2 α+1/(2 σ^2))\exp[(-(x-α)^2+(x-μ)/(2 σ^2))]+\\&(-2 x+2 β+1/(2σ^2))\exp[(-(x-β)^2+(x-μ)/(2 σ^2))]=0\end{align*}$
I have already used Wolfram, but it calculates the solution for $\sigma$, and other solvers say that they "Can not solve for x". Does anyone have an idea? Thank you all, in advance, for your concern.
P.S. Can I say that if this equation is equal to $0$, then only $(-2x+2 α+1/(2 σ^2))=0$ and $(-2 x+2 β+1/(2σ^2))=0$ at the same time, since exp is always $>0$.