Hey Petko.
Hint: Try letting u = e^(-0.1x) and you'll get a polynomial and then see if you can get a kind of "completed square" form for the equation (I'm just throwing ideas your way not giving a solution).
I have solved the following equation: 85e^(-2x) + 25e^(-0.1x) - 10 = 0 by using One point iteration and Newton Raphson's methods but I need the analytical solution in order to find the true answer. Can someone guide me through the steps for solving it? Thank you!