Question 916626
{{{ h = -16t^2 + 30t + 5 }}}
When the object hits the ground, the 
height above ground = zero, so
{{{ h = 0 }}}
{{{ -16t^2 + 30t + 5 = 0 }}}
Solve using the quadratic formula
{{{ h = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -16 }}}
{{{ b = 30 }}}
{{{ c = 5 }}}
{{{ t = ( -30 +- sqrt( 30^2 - 4*(-16)*5 )) / (2*(-16)) }}}
{{{ t = ( -30 +- sqrt( 900 + 320 )) / (-32)) }}}
{{{ t = ( -30 +- sqrt( 1220 )) / (-32)) }}}
{{{ t = ( -30 - 34.928) / (-32)) }}}
( The positive root does not work here )
{{{ t = ( -64.928 ) / ( -32 ) }}}
{{{ t = 2.029 }}}
The object hits the ground in 2.029 sec
Here's the plot:
{{{ graph( 400, 400, -1, 3, -2, 20, -16x^2 + 30x + 5 ) }}}