Apparently you are trying to see how many seconds the object in question would take to return to earth. The velocity equation is:
If you integrate with respect to t, you get
x = int(v,t) = -a*t^2/2+b*t
The solution is either t = 0 (the beginning) or t = b/(2*a) (at the end.) Your mistake was twofold. You had a positive value for a, and you didn't include the 1/2.