2.5t^2-12t+8=0

Solution for 2.5t^2-12t+8=0 equation:

Simplifying
2.5t2 + -12t + 8 = 0

Reorder the terms:
8 + -12t + 2.5t2 = 0

Solving
8 + -12t + 2.5t2 = 0

Solving for variable 't'.

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

Divide each side by '2.5'.
3.2 + -4.8t + t2 = 0

Move the constant term to the right:

Add '-3.2' to each side of the equation.
3.2 + -4.8t + -3.2 + t2 = 0 + -3.2

Reorder the terms:
3.2 + -3.2 + -4.8t + t2 = 0 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + -4.8t + t2 = 0 + -3.2
-4.8t + t2 = 0 + -3.2

Combine like terms: 0 + -3.2 = -3.2
-4.8t + t2 = -3.2

The t term is -4.8t.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8t + 5.76 + t2 = -3.2 + 5.76

Reorder the terms:
5.76 + -4.8t + t2 = -3.2 + 5.76

Combine like terms: -3.2 + 5.76 = 2.56
5.76 + -4.8t + t2 = 2.56

Factor a perfect square on the left side:
(t + -2.4)(t + -2.4) = 2.56

Calculate the square root of the right side: 1.6

Break this problem into two subproblems by setting 
(t + -2.4) equal to 1.6 and -1.6.

Subproblem 1
t + -2.4 = 1.6

Simplifying
t + -2.4 = 1.6

Reorder the terms:
-2.4 + t = 1.6

Solving
-2.4 + t = 1.6

Solving for variable 't'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + t = 1.6 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + t = 1.6 + 2.4
t = 1.6 + 2.4

Combine like terms: 1.6 + 2.4 = 4
t = 4

Simplifying
t = 4

Subproblem 2
t + -2.4 = -1.6

Simplifying
t + -2.4 = -1.6

Reorder the terms:
-2.4 + t = -1.6

Solving
-2.4 + t = -1.6

Solving for variable 't'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + t = -1.6 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + t = -1.6 + 2.4
t = -1.6 + 2.4

Combine like terms: -1.6 + 2.4 = 0.8
t = 0.8

Simplifying
t = 0.8

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4, 0.8}