Pretty good attempt.
1) One error. You need y = 1/2 when x = 0 and you don't have that. A little experimentation shows that the phase shift should be +5/8.
2) Solve away. You will need a calculator. Set the whole expression equal to 50 and find the two solutions in the first trip around. Other solutions should follow by 2.5 minutes. I get 0.97335 and 1.52665. It appears I agree with the given solution.