Substitute 240 ft as the height h in the equation:



Get 0 on the right:  



Divide every term by 





Factor the left side:



Set each factor = 0

Setting  

Setting 
        

There are two solutions, because the
object will be exactly 240 feet above
the ground on its way UP exactly 3 
seconds after it is projected upward. 
Then it will be 240 feet above the ground 
again on its way back DOWN 5 seconds 
after it is projected upward.  So the 
answer is both 3 seconds and 5 seconds
after it is projected upward.

Edwin