And how did you derive that equation for risk of ruin? What are the details? Which of course is always the next thing to ask to be safe about the numerical answer anyway.
You can always plot it by the way in excel (in 0,1 range) to visually see what a good starting guess is and then go as BruceZ suggested or try the Mathematica version.
Also recognizing the answer ought to be small you can also do it using Taylor expansion (level 2) around 0. This gives a quadratic for x that you can solve and get something like 0.064 that you can then use as a new Taylor expansion point for the exponentials and obtain instantly another quadratic that is giving 0.0803. A third time is not needed at least to 2 digits accuracy but can be done for fun too. Of course none of this is needed, i am only suggesting how to kill time in an airport (with no interesting people around) if you have only paper and a calculator (lol) or a new laptop with no internet connection in a bus ride with no wifi. Finally you can also rederive some derivative approximation solutions for general functions F in the bus ride (assuming its not a bumpy one!)
These days even some cheap $15 calculators have the ability to program functions into them so that you can then numerically get the answer by trial and error in less than 1 min after inputing the monstrous long expression of course first.
(kind of a mathematician's hunt in the wild with primitive weapons survivalist challenge)