5t^2-6t+1.8=0

Solution for 5t^2-6t+1.8=0 equation:

Simplifying
5t2 + -6t + 1.8 = 0

Reorder the terms:
1.8 + -6t + 5t2 = 0

Solving
1.8 + -6t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
0.36 + -1.2t + t2 = 0

Move the constant term to the right:

Add '-0.36' to each side of the equation.
0.36 + -1.2t + -0.36 + t2 = 0 + -0.36

Reorder the terms:
0.36 + -0.36 + -1.2t + t2 = 0 + -0.36

Combine like terms: 0.36 + -0.36 = 0.00
0.00 + -1.2t + t2 = 0 + -0.36
-1.2t + t2 = 0 + -0.36

Combine like terms: 0 + -0.36 = -0.36
-1.2t + t2 = -0.36

The t term is -1.2t.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2t + 0.36 + t2 = -0.36 + 0.36

Reorder the terms:
0.36 + -1.2t + t2 = -0.36 + 0.36

Combine like terms: -0.36 + 0.36 = 0.00
0.36 + -1.2t + t2 = 0.00

Factor a perfect square on the left side:
(t + -0.6)(t + -0.6) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(t + -0.6) equal to 0.00 and 0.00.

Subproblem 1
t + -0.6 = 0.00

Simplifying
t + -0.6 = 0.00

Reorder the terms:
-0.6 + t = 0.00

Solving
-0.6 + t = 0.00

Solving for variable 't'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + t = 0.00 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + t = 0.00 + 0.6
t = 0.00 + 0.6

Combine like terms: 0.00 + 0.6 = 0.6
t = 0.6

Simplifying
t = 0.6

Subproblem 2
t + -0.6 = 0.00

Simplifying
t + -0.6 = 0.00

Reorder the terms:
-0.6 + t = 0.00

Solving
-0.6 + t = 0.00

Solving for variable 't'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + t = 0.00 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + t = 0.00 + 0.6
t = 0.00 + 0.6

Combine like terms: 0.00 + 0.6 = 0.6
t = 0.6

Simplifying
t = 0.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.6, 0.6}