Answer
2.3 seconds
Work Step by Step
$h=-16t^2-20t+180$
$50=-16t^2-20t+180$
$0=-16t^2-20t+130$
$x=(-x±\sqrt {b^2-4ac})/2a$
$x=(-(-20)±\sqrt {(-20)^2-4*-16*130})/2*(-16)$
$x=(20±\sqrt {400+64*130})/-32$
$x=(20±\sqrt {400+8320})/-32$
$x=(20±\sqrt {8720})/-32$
$x=(20±93.38)/-32$
We are talking about height, so we want only the positive value of $x$. However, since the denominator is negative, we want the negative value of the square root.
$x=(20±93.38)/-32$
$x=(20-93.38)/-32$
$x=-73.38/-32$
$x=2.29$
