6x^2-18x+7=0

Solution for 6x^2-18x+7=0 equation:

Simplifying
6x2 + -18x + 7 = 0

Reorder the terms:
7 + -18x + 6x2 = 0

Solving
7 + -18x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
1.166666667 + -3x + x2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + -3x + -1.166666667 + x2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + -3x + x2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + -3x + x2 = 0 + -1.166666667
-3x + x2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
-3x + x2 = -1.166666667

The x term is -3x.  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.
-3x + 2.25 + x2 = -1.166666667 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -1.166666667 + 2.25

Combine like terms: -1.166666667 + 2.25 = 1.083333333
2.25 + -3x + x2 = 1.083333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.083333333

Calculate the square root of the right side: 1.040833

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.040833 and -1.040833.

Subproblem 1
x + -1.5 = 1.040833

Simplifying
x + -1.5 = 1.040833

Reorder the terms:
-1.5 + x = 1.040833

Solving
-1.5 + x = 1.040833

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.040833 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.040833 + 1.5
x = 1.040833 + 1.5

Combine like terms: 1.040833 + 1.5 = 2.540833
x = 2.540833

Simplifying
x = 2.540833

Subproblem 2
x + -1.5 = -1.040833

Simplifying
x + -1.5 = -1.040833

Reorder the terms:
-1.5 + x = -1.040833

Solving
-1.5 + x = -1.040833

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.040833 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.040833 + 1.5
x = -1.040833 + 1.5

Combine like terms: -1.040833 + 1.5 = 0.459167
x = 0.459167

Simplifying
x = 0.459167

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.540833, 0.459167}