Is it possible to solve for $x$ which satisfies the equation $$d=(a\exp(bx)+\exp(cx))x^2$$ where $a,b,c,d$ are given constants? It looks quite horrible... Many thanks!
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Looks doubtful; you have the sum of two independent exponentials in there, which precludes the use of things like the Lambert function... – J. M. ain't a mathematician Aug 24 '12 at 13:28
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Yes, it is quite horrible. It is not possible in terms of elementary functions. Numerical procedures are always available. And, at least for limited ranges for the parameters, there may be good approximate formulas. – André Nicolas Aug 24 '12 at 13:30