5t^2-14t+6=0

Solution for 5t^2-14t+6=0 equation:

Simplifying
5t2 + -14t + 6 = 0

Reorder the terms:
6 + -14t + 5t2 = 0

Solving
6 + -14t + 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'.
1.2 + -2.8t + t2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -2.8t + -1.2 + t2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -2.8t + t2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -2.8t + t2 = 0 + -1.2
-2.8t + t2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-2.8t + t2 = -1.2

The t term is -2.8t.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8t + 1.96 + t2 = -1.2 + 1.96

Reorder the terms:
1.96 + -2.8t + t2 = -1.2 + 1.96

Combine like terms: -1.2 + 1.96 = 0.76
1.96 + -2.8t + t2 = 0.76

Factor a perfect square on the left side:
(t + -1.4)(t + -1.4) = 0.76

Calculate the square root of the right side: 0.871779789

Break this problem into two subproblems by setting 
(t + -1.4) equal to 0.871779789 and -0.871779789.

Subproblem 1
t + -1.4 = 0.871779789

Simplifying
t + -1.4 = 0.871779789

Reorder the terms:
-1.4 + t = 0.871779789

Solving
-1.4 + t = 0.871779789

Solving for variable 't'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + t = 0.871779789 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + t = 0.871779789 + 1.4
t = 0.871779789 + 1.4

Combine like terms: 0.871779789 + 1.4 = 2.271779789
t = 2.271779789

Simplifying
t = 2.271779789

Subproblem 2
t + -1.4 = -0.871779789

Simplifying
t + -1.4 = -0.871779789

Reorder the terms:
-1.4 + t = -0.871779789

Solving
-1.4 + t = -0.871779789

Solving for variable 't'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + t = -0.871779789 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + t = -0.871779789 + 1.4
t = -0.871779789 + 1.4

Combine like terms: -0.871779789 + 1.4 = 0.528220211
t = 0.528220211

Simplifying
t = 0.528220211

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.271779789, 0.528220211}