I have this non linear equation: $$-(a+c\,e)\left(e^{-\frac{b}{a+c\,e}}-1\right)-c\,d=f$$ The only unknown is $c$. All the coefficients ($a$, $b$, $c$, $d$, $f$) are real non-null costants.
How can I find $c$? Do you have some idea?
2026-03-25 13:59:51.1774447191
How to solve the non-linear equation $-(a+c\,e)\left(\exp(-b/(a+c\,e))-1\right)-c\,d=f$ for $c$?
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The first thing you do with an equation like that, is to get rid of extra complexity. Put $x=b/(a+ce^1)$, then the equation for the new unknown $x$ has the form $$e^{-x}=\alpha+\beta x$$ where you can express $\alpha$ and $\beta$ in terms of the other parameters of the problem. This is a transcendental equation with no solution in terms of simple functions. Your best bet is most likely to solve it numerically. You can also express the solution in terms of Lambert's W function, but depending on what you need this for, that might well be overkill.