As you said, multiply through by 2







That is a quadratic equation, so we use the
quadratic formula:

 

with x = t, a = g, b = 2v0, and c = -2h

 













There are two solutions.  

 and 

The given equation is for the time when an object projected upward from the
ground is at a certain height h.  It is at that height h once going up and
once again coming down.  The first solution is for the time when the ball
first reaches height h going up, and the second is for the time when it
reaches that same height h coming down.   

Edwin