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How do I solve the equation below for $x$? $A$, $B$, $a$ and $r$ are constants.

\begin{equation} x + \frac{1}{1+Ar^{-x/a}} + B =0 \end{equation}

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migrated from meta.math.stackexchange.com Mar 4 '13 at 10:59

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I assume you meant to post this on the main site, not here on meta. –  Ilmari Karonen Mar 4 '13 at 10:24
    
Instead of closing, I vote for migration to our main site. –  Jyrki Lahtonen Mar 4 '13 at 10:33
    
@JyrkiLahtonen: I would've done that, but couldn't find the option. Did I just miss it, or can we no longer migrate posts to the main site from meta without bothering the mods? –  Ilmari Karonen Mar 4 '13 at 10:36
    
How could i transfer the question to main site? –  Norman Mar 4 '13 at 10:45
1  
I don't think you can solve it analytically. But sure you can numerically, for given values of $a,A,B$ and $r$ of course. –  Kaster Mar 4 '13 at 11:26

1 Answer 1

up vote 1 down vote accepted

Answer: yes.

This equation is hard to solve (symbolically).

Even in the simple case $$ x+\frac{1}{1+e^{-x}}=0 $$ with solution $x \approx -0.401058137541547$, it is identified by the ISC only as "solution of $z+W(z+1)=0$" where $W$ is the Lambert W function.

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