0=-5t^2+15t-11.2

Solution for 0=-5t^2+15t-11.2 equation:

Simplifying
0 = -5t2 + 15t + -11.2

Reorder the terms:
0 = -11.2 + 15t + -5t2

Solving
0 = -11.2 + 15t + -5t2

Solving for variable 't'.

Combine like terms: 0 + 11.2 = 11.2
11.2 + -15t + 5t2 = -11.2 + 15t + -5t2 + 11.2 + -15t + 5t2

Reorder the terms:
11.2 + -15t + 5t2 = -11.2 + 11.2 + 15t + -15t + -5t2 + 5t2

Combine like terms: -11.2 + 11.2 = 0.0
11.2 + -15t + 5t2 = 0.0 + 15t + -15t + -5t2 + 5t2
11.2 + -15t + 5t2 = 15t + -15t + -5t2 + 5t2

Combine like terms: 15t + -15t = 0
11.2 + -15t + 5t2 = 0 + -5t2 + 5t2
11.2 + -15t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
11.2 + -15t + 5t2 = 0

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

Divide each side by '5'.
2.24 + -3t + t2 = 0

Move the constant term to the right:

Add '-2.24' to each side of the equation.
2.24 + -3t + -2.24 + t2 = 0 + -2.24

Reorder the terms:
2.24 + -2.24 + -3t + t2 = 0 + -2.24

Combine like terms: 2.24 + -2.24 = 0.00
0.00 + -3t + t2 = 0 + -2.24
-3t + t2 = 0 + -2.24

Combine like terms: 0 + -2.24 = -2.24
-3t + t2 = -2.24

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -2.24 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -2.24 + 2.25

Combine like terms: -2.24 + 2.25 = 0.01
2.25 + -3t + t2 = 0.01

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(t + -1.5) equal to 0.1 and -0.1.

Subproblem 1
t + -1.5 = 0.1

Simplifying
t + -1.5 = 0.1

Reorder the terms:
-1.5 + t = 0.1

Solving
-1.5 + t = 0.1

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 0.1 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 0.1 + 1.5
t = 0.1 + 1.5

Combine like terms: 0.1 + 1.5 = 1.6
t = 1.6

Simplifying
t = 1.6

Subproblem 2
t + -1.5 = -0.1

Simplifying
t + -1.5 = -0.1

Reorder the terms:
-1.5 + t = -0.1

Solving
-1.5 + t = -0.1

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -0.1 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -0.1 + 1.5
t = -0.1 + 1.5

Combine like terms: -0.1 + 1.5 = 1.4
t = 1.4

Simplifying
t = 1.4

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.6, 1.4}