# Solve for t h=-16t^2+64t+80

h=-16t2+64t+80
Rewrite the equation as -16t2+64t+80=h.
-16t2+64t+80=h
Move h to the left side of the equation by subtracting it from both sides.
-16t2+64t+80-h=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=-16, b=64, and c=80-h into the quadratic formula and solve for t.
-64±642-4⋅(-16⋅(80-h))2⋅-16
Simplify.
Simplify the numerator.
Raise 64 to the power of 2.
t=-64±4096-4⋅(-16⋅(80-h))2⋅-16
Apply the distributive property.
t=-64±4096-4⋅(-16⋅80-16(-h))2⋅-16
Multiply -16 by 80.
t=-64±4096-4⋅(-1280-16(-h))2⋅-16
Multiply -1 by -16.
t=-64±4096-4⋅(-1280+16h)2⋅-16
Apply the distributive property.
t=-64±4096-4⋅-1280-4(16h)2⋅-16
Multiply -4 by -1280.
t=-64±4096+5120-4(16h)2⋅-16
Multiply 16 by -4.
t=-64±4096+5120-64h2⋅-16
t=-64±9216-64h2⋅-16
Factor 64 out of 9216-64h.
Factor 64 out of 9216.
t=-64±64(144)-64h2⋅-16
Factor 64 out of -64h.
t=-64±64(144)+64(-h)2⋅-16
Factor 64 out of 64(144)+64(-h).
t=-64±64(144-h)2⋅-16
t=-64±64(144-h)2⋅-16
Rewrite 64(144-h) as 82(122-h).
Rewrite 64 as 82.
t=-64±82(144-h)2⋅-16
Rewrite 144 as 122.
t=-64±82(122-h)2⋅-16
t=-64±82(122-h)2⋅-16
Pull terms out from under the radical.
t=-64±8122-h2⋅-16
Raise 12 to the power of 2.
t=-64±8144-h2⋅-16
t=-64±8144-h2⋅-16
Multiply 2 by -16.
t=-64±8144-h-32
Simplify -64±8144-h-32.
t=8±144-h4
t=8±144-h4
The final answer is the combination of both solutions.
t=8+144-h4
t=8-144-h4
Solve for t h=-16t^2+64t+80