I'm trying to solve a calc 1 problem about how long it takes to fill a reservoir. This is the result of my integration.

$$20t + \frac{240}{\pi} \sin\frac{\pi t}{12}=2500$$ 

I know the answer is $t = 122.6$ (its an odd book problem), I only figured it out because I used my graphing calculator and found the intersection of the function and $y=2500$.

How can I solve for $t$ by hand?