Using this equation, we want to solve for the variable t, for time. It is given that the height is 5 meters, therefore, h = 5. Then, we plug that into the given equation and solve for t
h = 2 + 9t - 5t²
5 = 2 + 9t - 5t² ← Reorder this to make it easier to factor
5 = -5t² + 9t + 2
0 = -5t² + 9t + 2 - 5
0 = -5t² + 9t - 3 ← We want to solve for t. We can either complete the square, or use the quadratic formula. I will be using the quadratic formula, which is:
[tex] t = \frac{-b+\sqrt{b^2-4ac}}{2a} [/tex] AND [tex] t = \frac{-b-\sqrt{b^2-4ac}}{2a} [/tex] where a = -5, b = 9, and c = -3
Then, you can plug this into your calculator, and
t = (-9 + √141)/10 ≈ 0.29
t = (-9 - √141)/10 ≈ -2.09
