You have two options. (1/2)mv^2 = mgh so (1/2)v^2 = gh
Rearranging, you get h = v^2/2g so you can work it out that way.
Using suvat, you want s, have u, v and a and don't need t. The equation is v^2 = u^2 + 2as.
Rearranging, you get s = (v^2 - u^2)/2a. As v^2 = 0 this simplifies to exactly what you have above, just with different letters.