0=-5t^2+10t+1.2

Solution for 0=-5t^2+10t+1.2 equation:

Simplifying
0 = -5t2 + 10t + 1.2

Reorder the terms:
0 = 1.2 + 10t + -5t2

Solving
0 = 1.2 + 10t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -1.2 = -1.2
-1.2 + -10t + 5t2 = 1.2 + 10t + -5t2 + -1.2 + -10t + 5t2

Reorder the terms:
-1.2 + -10t + 5t2 = 1.2 + -1.2 + 10t + -10t + -5t2 + 5t2

Combine like terms: 1.2 + -1.2 = 0.0
-1.2 + -10t + 5t2 = 0.0 + 10t + -10t + -5t2 + 5t2
-1.2 + -10t + 5t2 = 10t + -10t + -5t2 + 5t2

Combine like terms: 10t + -10t = 0
-1.2 + -10t + 5t2 = 0 + -5t2 + 5t2
-1.2 + -10t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-1.2 + -10t + 5t2 = 0

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

Divide each side by '5'.
-0.24 + -2t + t2 = 0

Move the constant term to the right:

Add '0.24' to each side of the equation.
-0.24 + -2t + 0.24 + t2 = 0 + 0.24

Reorder the terms:
-0.24 + 0.24 + -2t + t2 = 0 + 0.24

Combine like terms: -0.24 + 0.24 = 0.00
0.00 + -2t + t2 = 0 + 0.24
-2t + t2 = 0 + 0.24

Combine like terms: 0 + 0.24 = 0.24
-2t + t2 = 0.24

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 0.24 + 1

Reorder the terms:
1 + -2t + t2 = 0.24 + 1

Combine like terms: 0.24 + 1 = 1.24
1 + -2t + t2 = 1.24

Factor a perfect square on the left side:
(t + -1)(t + -1) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(t + -1) equal to 1.113552873 and -1.113552873.

Subproblem 1
t + -1 = 1.113552873

Simplifying
t + -1 = 1.113552873

Reorder the terms:
-1 + t = 1.113552873

Solving
-1 + t = 1.113552873

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 1.113552873 + 1

Combine like terms: -1 + 1 = 0
0 + t = 1.113552873 + 1
t = 1.113552873 + 1

Combine like terms: 1.113552873 + 1 = 2.113552873
t = 2.113552873

Simplifying
t = 2.113552873

Subproblem 2
t + -1 = -1.113552873

Simplifying
t + -1 = -1.113552873

Reorder the terms:
-1 + t = -1.113552873

Solving
-1 + t = -1.113552873

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -1.113552873 + 1

Combine like terms: -1 + 1 = 0
0 + t = -1.113552873 + 1
t = -1.113552873 + 1

Combine like terms: -1.113552873 + 1 = -0.113552873
t = -0.113552873

Simplifying
t = -0.113552873

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.113552873, -0.113552873}