Am I able to find the initial velocity using only gravity and height

This is part of a longer problem, but I must first find the initial velocity. A ball is thrown into the air with a max height of 20.4 m.
How do you find the initial velocity without a given time?

My first guess at the time was 1.44279 sec, using questionable methods, and it does not give the right answers.

By v^2 = u^2 - 2gh
=>0 = u^2 - 2 x 9.8 x 20.4
=>u = √399.84
=>u = 19.99 m/s

first solve for time with the position equation x = x0 + v0*t + 1/2*a*t^2 where x0 = 0, v0 = 0 a = 9.81

then solve for v0 with the velocity equation v = v0 +a*t