Answer
t=2.3 s
Work Step by Step
$$h = -16t^2-20t+180$$
We want to consider when h=50, so:
$$0 = -16t^2-20t+130$$
We use the quadratic formula
$$t= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$
Where b is the coefficient of the term with a variable raised to the first power, a is the coefficient of the squared term, and c is the coefficient of the term without a variable in front of it.
We now solve, considering only the positive value, to have:
t=2.3 s
