Wow , it is very difficult to solve by our hands ! By using my calculator , i got
Thanks - I didn't even notice that N = 0 would be a solution!
The equation has come up as I posed a question to myself asking after how many months a reducing balance depreciation methodology (accounting related) would have depreciated a piece of equipment as much as a straight line depreciation methodology.
It has another solution where N > 0 that is approximately 35.1 (found by using a spreadsheet), which is the solution I was aiming to explain by re-arranging the equation.
I'm quite glad it wasn't just a simple re-arrangement and that I'm (hopefully) not missing a basic trick!