The reason you cannot get a simple answer for t (time) (e.g. t = 10 seconds) is because you appear to have not been supplied a value for h (height). This formula gives you the time given the height, or the height given the time., but you cannot solve for a variable if there are two unknown variables. If you have not been given an h value then the answer will have to be in terms of h. As in, "The time taken to reach the water would be the height times x plus y".
The quadratic formula will give us the time required for Joe to reach the water when his height is 0. This doesn't seem to be useful information, as Joe has already reached the water when he is 0 distance away from it, nevertheless, since the question directs us to use the quadratic formula, compare your answer here.
a = -16
b = 15
c = 12
(-15 +- sqrt(225 + 768)) / -32 = +1.4535 or - .516
If you received these answers, congratulations! You did apply the quadratic formula correctly and found out that the time it takes for Joe to reach the water at a height of 0 is 1.4535. However, you're right that this question doesn't seem to make much sense, so feel free to inquire about it to your teacher.
As an aside when you aren't given any units it is fair practice to assume common units, for example, meters or seconds, as you did, or simply to denote unitless.