I have been out of eduacation for while so am a bit rusty on my maths, but basically I started with a binomial expansion and have windled it down to the following alebraic equation which i cant seem to simplify anymore!

(n/9)*0.9^n + 0.9^n = 0.5

And obviously im trying to find n, which I know is around 16.5, but only through guessing!