Your problem is this:
You want to find x, which is the time in years it took to reach the initial investment. That is how I would go about it, but that uses definite integration instead of indefinite. Does this make sense to you?
edit: The equation you gave for the savings indicates that at t=0, the savings is already $20k because e^0 is 1. If that is true, then I suppose you need to find when the integral equals $210,000. I'll think about this some more. Didn't want to give you an incorrect answer though.