Question 417597
{{{d = -16t^2 + 96t}}}
It will help to think of the equation this way:
Gravity acts in a downward direction, so the term {{{-16t^2}}}
is the only thing that can represent gravity.
The other term {{{96t}}} is the only thing that can represent 
the distance caused by the upward throwing force.
{{{128 = -16t^2 + 96t}}}
Divide both sides by {{{16}}}
{{{-t^2 + 6t = 8}}}
{{{-t^2 + 6t - 8 = 0}}}
Use quadratic formula
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = -1}}}
{{{b = 6}}}
{{{c = -8}}}
{{{t = (-6 +- sqrt( 6^2-4*(-1)*(-8) ))/(2*(-1)) }}}
{{{t = (-6 +- sqrt( 36 - 32 ))/(-2) }}}
{{{t = ( -6 - 2 ) / (-2) }}}
{{{t = 4 }}} sec  (the other root gives a negative for {{{t}}})