Question 539247
You need to find the larger of 2 roots by
setting the equation equal to zero
{{{ -16t^2 + 46t + 6 = 0 }}}
{{{ -8t^2 + 23t + 3 = 0 }}}
Use the quadratic formula
{{{ t  = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = -8 }}}
{{{ b = 23 }}}
{{{ c = 3 }}}
{{{ t = (-23 +- sqrt( 23^2-4*(-8)*3 ))/(2*(-8)) }}}
{{{ t = (-23 +- sqrt( 529 + 96 )) / (-16) }}}
{{{ t = (-23 +- sqrt( 625 )) / (-16) }}} 
{{{ t = ( -23 + 25 ) / (-16) }}}
{{{ t = -1/8 }}} ( can't use negative time )
and, taking the (-) square root,
{{{ t = ( -23 - 25 ) / (-16) }}} 
{{{ t = (-48)/(-16) = 3 }}}
It will hit the ground in 3 sec