x=14x^2+7x-6

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

Simplifying
x = 14x2 + 7x + -6

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

Solving
x = -6 + 7x + 14x2

Solving for variable 'x'.

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

Combine like terms: x + -7x = -6x
6 + -6x + -14x2 = -6 + 7x + 14x2 + 6 + -7x + -14x2

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

Combine like terms: -6 + 6 = 0
6 + -6x + -14x2 = 0 + 7x + -7x + 14x2 + -14x2
6 + -6x + -14x2 = 7x + -7x + 14x2 + -14x2

Combine like terms: 7x + -7x = 0
6 + -6x + -14x2 = 0 + 14x2 + -14x2
6 + -6x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
6 + -6x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -3x + -7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -3x + -7x2)' equal to zero and attempt to solve:

Simplifying
3 + -3x + -7x2 = 0

Solving
3 + -3x + -7x2 = 0

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

Divide each side by '-7'.
-0.4285714286 + 0.4285714286x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + 0.4285714286x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + 0.4285714286x + x2 = 0 + 0.4285714286
0.4285714286x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
0.4285714286x + x2 = 0.4285714286

The x term is 0.4285714286x.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286x + 0.04591836735 + x2 = 0.4285714286 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286x + x2 = 0.4285714286 + 0.04591836735

Combine like terms: 0.4285714286 + 0.04591836735 = 0.47448979595
0.04591836735 + 0.4285714286x + x2 = 0.47448979595

Factor a perfect square on the left side:
(x + 0.2142857143)(x + 0.2142857143) = 0.47448979595

Calculate the square root of the right side: 0.688832197

Break this problem into two subproblems by setting 
(x + 0.2142857143) equal to 0.688832197 and -0.688832197.

Subproblem 1
x + 0.2142857143 = 0.688832197

Simplifying
x + 0.2142857143 = 0.688832197

Reorder the terms:
0.2142857143 + x = 0.688832197

Solving
0.2142857143 + x = 0.688832197

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = 0.688832197 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = 0.688832197 + -0.2142857143
x = 0.688832197 + -0.2142857143

Combine like terms: 0.688832197 + -0.2142857143 = 0.4745464827
x = 0.4745464827

Simplifying
x = 0.4745464827

Subproblem 2
x + 0.2142857143 = -0.688832197

Simplifying
x + 0.2142857143 = -0.688832197

Reorder the terms:
0.2142857143 + x = -0.688832197

Solving
0.2142857143 + x = -0.688832197

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = -0.688832197 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = -0.688832197 + -0.2142857143
x = -0.688832197 + -0.2142857143

Combine like terms: -0.688832197 + -0.2142857143 = -0.9031179113
x = -0.9031179113

Simplifying
x = -0.9031179113

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4745464827, -0.9031179113}
Solution
x = {0.4745464827, -0.9031179113}