7x^2-14x+6=0

Solution for 7x^2-14x+6=0 equation:

Simplifying
7x2 + -14x + 6 = 0

Reorder the terms:
6 + -14x + 7x2 = 0

Solving
6 + -14x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
0.8571428571 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + -2x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + -2x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.8571428571
-2x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
-2x + x2 = -0.8571428571

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

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.8571428571 + 1

Reorder the terms:
1 + -2x + x2 = -0.8571428571 + 1

Combine like terms: -0.8571428571 + 1 = 0.1428571429
1 + -2x + x2 = 0.1428571429

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.1428571429

Calculate the square root of the right side: 0.377964473

Break this problem into two subproblems by setting 
(x + -1) equal to 0.377964473 and -0.377964473.

Subproblem 1
x + -1 = 0.377964473

Simplifying
x + -1 = 0.377964473

Reorder the terms:
-1 + x = 0.377964473

Solving
-1 + x = 0.377964473

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.377964473 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.377964473 + 1
x = 0.377964473 + 1

Combine like terms: 0.377964473 + 1 = 1.377964473
x = 1.377964473

Simplifying
x = 1.377964473

Subproblem 2
x + -1 = -0.377964473

Simplifying
x + -1 = -0.377964473

Reorder the terms:
-1 + x = -0.377964473

Solving
-1 + x = -0.377964473

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.377964473 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.377964473 + 1
x = -0.377964473 + 1

Combine like terms: -0.377964473 + 1 = 0.622035527
x = 0.622035527

Simplifying
x = 0.622035527

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.377964473, 0.622035527}