Question 4263
Given the formula {{{h = 50 t - 5t^2}}}, the question is when will h=100 meters.


{{{100 = 50t - 5t^2}}}


Since this is a quadratic equation, you must set it equal to zero by moving everything either to the left side or the right side.  My preference, in order to eliminate the negative coefficient of {{{t^2}}} is to move everything to the left side.  In other words, add {{{+5t^2}}} and {{{-50t}}} to each side. 


Writing this with the highest powers of x first, it gives you 
{{{5t^2 - 50t + 100 = 0}}}


Divide both sides of the equation by 5:
{{{t^2 - 10t + 20 = 0}}}


Solve by completing the square or quadratic formula.  Completing the square is easier in this case.
{{{t^2 - 10t + _____ = -20 + ______}}}


Take half of the -10 (which is -5) and square (which is 25), so you must add 25 to each side of the equation.
{{{t^2 - 10t + 25  = -20 + 25}}}
{{{  (t-5)^2 = 5 }}}


Take the square root of each side of the equation:
{{{ (t - 5) = 0 +- sqrt (5) }}}


Add +5 to each side of the equation:
{{{ t - 5 + 5  = 0 + 5 +- sqrt (5) }}}
{{{ t = 5 +- sqrt (5) }}}


Of course the smaller of these values is the time to reach 100 meters going up, and the larger of these values is the time required to reach 100 meters coming back down.   {{{t = 5 - sqrt (5) }}} is the time required to get UP to 100 meters, and  {{{t = 5 + sqrt (5) }}} (which is about 7.2 seconds) is the time required to reach 100 meters on the way down.