-16t^2+40t-24.64=0

Solution for -16t^2+40t-24.64=0 equation:

Simplifying
-16t2 + 40t + -24.64 = 0

Reorder the terms:
-24.64 + 40t + -16t2 = 0

Solving
-24.64 + 40t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
1.54 + -2.5t + t2 = 0

Move the constant term to the right:

Add '-1.54' to each side of the equation.
1.54 + -2.5t + -1.54 + t2 = 0 + -1.54

Reorder the terms:
1.54 + -1.54 + -2.5t + t2 = 0 + -1.54

Combine like terms: 1.54 + -1.54 = 0.00
0.00 + -2.5t + t2 = 0 + -1.54
-2.5t + t2 = 0 + -1.54

Combine like terms: 0 + -1.54 = -1.54
-2.5t + t2 = -1.54

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = -1.54 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = -1.54 + 1.5625

Combine like terms: -1.54 + 1.5625 = 0.0225
1.5625 + -2.5t + t2 = 0.0225

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 0.0225

Calculate the square root of the right side: 0.15

Break this problem into two subproblems by setting 
(t + -1.25) equal to 0.15 and -0.15.

Subproblem 1
t + -1.25 = 0.15

Simplifying
t + -1.25 = 0.15

Reorder the terms:
-1.25 + t = 0.15

Solving
-1.25 + t = 0.15

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = 0.15 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = 0.15 + 1.25
t = 0.15 + 1.25

Combine like terms: 0.15 + 1.25 = 1.4
t = 1.4

Simplifying
t = 1.4

Subproblem 2
t + -1.25 = -0.15

Simplifying
t + -1.25 = -0.15

Reorder the terms:
-1.25 + t = -0.15

Solving
-1.25 + t = -0.15

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = -0.15 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = -0.15 + 1.25
t = -0.15 + 1.25

Combine like terms: -0.15 + 1.25 = 1.1
t = 1.1

Simplifying
t = 1.1

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.4, 1.1}