A ball is thrown from an initial height of 2 meters with an initial upward velocity of 20 m/s. The ball's height h (in meters) after t seconds is given by the following. h=2+20 t-5 t^2 Find all values of t for which the ball's height is 7 meters.

Step 1 ：The problem is asking for the time(s) at which the ball reaches a height of 7 meters. This is a quadratic equation problem. We can solve it by setting the equation equal to 7 and solving for t.

Step 2 ：The quadratic formula will be used to solve for t. The quadratic formula is given by: \[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where a, b, and c are coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

Step 3 ：In this case, a = -5, b = 20, and c = 2 - 7 = -5.

Step 4 ：Substituting these values into the quadratic formula, we get two possible values for t.

Step 5 ：The times at which the ball reaches a height of 7 meters are \(\boxed{0.27 \, \text{seconds}}\) and \(\boxed{3.73 \, \text{seconds}}\).