Unable to find explicit solution using solve function

Hello,

I am trying to solve for a rise time using the following equation. I am getting the error below when I run the code. I have tried rewriting this equation several ways in hopes of getting an explicit value but still haven't found a way that works yet. Please let me know of a possible solution if one such solution does exist. Thank you!

if true
  eqn = t_rise*((2*exp(-(200000*t_rise)/L))/5 - 7/5) == 
  92206878437459119621/5902958103587056517120000;

    sol = solve(eqn, t_rise);
end

Yields the following output

 if true 
    Warning: Unable to find explicit solution. For options, see help. 
    > In solve (line 317) 

    ans =

    Empty sym: 0-by-1
 end

Answer 1

[Steven Beumer]

You might want to have a look at the productlog function to get an analytic solution without solve. You could fill in the general equation in wolfram alpha and get an analytic solution that you can use. Like : http://www.wolframalpha.com/input/?i=c*x*exp(-b*x)-d+%3D+a