I need help with my math homework please anyone

Question

2-An object is thrown upward at a speed of 61 feet per second by a machine from a height of 6 feet off the ground. The height  of the object after t seconds can be found using the equation 

h=−16t2+61t+6

a) When will the height be 27 feet?

b)When will the object reach the ground?

Answer 1

h(t) = -16t² + 61t + 6

(a)

Set h(t)=27 and solve for t.

-16t² + 61t + 6 = 27 ⇒

-16t² + 61t - 21 = 0

Solve this quadratic equation for t using the quadratic formula. You will get 2 positive solutions. The smaller solution is the time it takes to reach 27 ft on the way up. The larger solution is the time it takes to reach 27 ft on the way down.

(b)

Set h(t)=0 and solve for t using the quadratic formula.

-16t² + 61t + 6 = 0

You will get a negative and a positive solution for t. Since time starts at t=0, the positive solution is the correct one. You have everything you need, just do the algebra and finish from here.