Question 907494
  h = -3t^2 + 147
-3t^2 is a very rough approximation of the acceleration due to gravity
20.25ft = -3t^2 + 147 
In each step that you took you changed an important element of the equation.

h = 3t^2 + 147 here you changed gravity to a positive force making the paper plane rise and never fall
h(t) = 3^2 + 147 - 20.25 ft here you left out the time 
h(t) is the height
so plug in the 20.25 ft here
20.25 = -3t^2 + 147
 -126.75= -3t^2
42.25 =t^2
6.5=t
So after 6.5 second the plane is at 20.25 ft 
This is assuming that a breeze doesn't catch it and take it away