how to solve 9=-16t^2+24t+4?

9 = -16t^2 + 24t + 4
16t^2 - 24t - 4 + 9 = 0
16t^2 - 24t + 5 = 0
16t^2 - 4t - 20t + 5 = 0
(16t^2 - 4t) - (20t - 5) = 0
4t(4t - 1) - 5(4t - 1) = 0
(4t - 1)(4t - 5) = 0

4t - 1 = 0
4t = 1
t = 1/4 (0.25)

4t - 5 = 0
4t = 5
t = 5/4 (1.25)

∴ t = 1/4 (0.25), 5/4 (1.25)

16 t ² - 24 t + 5 = 0

( 4 t - 1 ) ( 4 t - 5 ) = 0

t = 1/4 , t = 5/4

t = 0.25 and 1.25

Move all the constants to one side
-9 = 16t^2 - 24t -4
-5 = 16t^2 - 24t
-5/16 = t^2 - 3t/2

take the coefficient of t divide it by 2 square it and add it to both sides
((3/2)/2)^2
(3/4)^2 = 9/16

now you can factor the equation
t^2 - 3t/2 + 9/16 = -5/16 + 9/16
(t-3/4)(t-3/4) = 4/16
(t-3/4)^2 = 4/16

take the square root of both sides in order to remove one of the factors on the left
sqrt(t-3/4)^2 = +-sqrt(4/16)
t-3/4 = +-1/2

t = 1/2 + 3/4 = 2/4 + 3/4 = 5/4
t = -1/2 + 3/4 = -2/4 + 3/4 = 1/4

9 = –16t² + 24t + 4
16t² – 24t – 4 + 9 = 0
16t² – 24t + 5 = 0
(4t – 5)(4t – 1) = 0
(4t – 5) = 0
4t = 5
t = 5/4
(4t – 1) = 0
4t = 1
t = 1/4
t = {1/4, 5/4}

16t^2 - 24t + 5 = 0
(4t - 5)(4t - 1) = 0
t = 5/4, 1/4

16t^2-24t+5=0
(4x-5)(4x-1)
x=5/4 or x = 1/4

Looks like the code for the Dharma Initiative. Get your calculator buddy. Your in for a doozy.

0.25 and 1.25