What was the source of your equation? What was your reasoning?
The basic equation for this sort of exercise is:
...where s is the height (in meters) at time t seconds, v_0 is the initial velocity, and h_0 is the initial height. You are given s(T) and s(T+2) = 0.
I'm not sure what is meant by "a decimal fraction of 0.5665 of the total time"...? Is this the exact text of the exercise?
Note: Since the object is "dropped", then v_0 = 0, so the equation reduces to: