Is it possible in general to solve equations of the form $Ae^{Bx}+Cx+D=0$? The most I have been able to do is rearrange the equation as $(Bx+\frac{BD}{C})=-\frac{AB}{C}e^{-\frac{BD}{C}}e^{(Bx+\frac{BD}{C})}$, which is in the form of $x=Ae^x$ for $(Bx+\frac{BD}{C})$ which looks solvable. However I don't know how. Any help appreciated.
2026-04-09 07:14:49.1775718889
Solving $Ae^{Bx}+Cx+D=0$
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Using Lambert W function, $x=a\mathrm e^x$ can be rewritten as $(-x)\mathrm e^{-x}=-a$, hence $x=-W(-a)$.
Note that this is not much more than a rewriting of the equation, hence the fact that Lambert W function was given a definition and that $x$ can be expressed through it does not lead us closer to a "solution", if you ask me.