0=3x^2-6+11x+14x^2-13x

Solution for 0=3x^2-6+11x+14x^2-13x equation:

Simplifying
0 = 3x2 + -6 + 11x + 14x2 + -13x

Reorder the terms:
0 = -6 + 11x + -13x + 3x2 + 14x2

Combine like terms: 11x + -13x = -2x
0 = -6 + -2x + 3x2 + 14x2

Combine like terms: 3x2 + 14x2 = 17x2
0 = -6 + -2x + 17x2

Solving
0 = -6 + -2x + 17x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + 2x + -17x2 = -6 + -2x + 17x2 + 6 + 2x + -17x2

Reorder the terms:
6 + 2x + -17x2 = -6 + 6 + -2x + 2x + 17x2 + -17x2

Combine like terms: -6 + 6 = 0
6 + 2x + -17x2 = 0 + -2x + 2x + 17x2 + -17x2
6 + 2x + -17x2 = -2x + 2x + 17x2 + -17x2

Combine like terms: -2x + 2x = 0
6 + 2x + -17x2 = 0 + 17x2 + -17x2
6 + 2x + -17x2 = 17x2 + -17x2

Combine like terms: 17x2 + -17x2 = 0
6 + 2x + -17x2 = 0

Begin completing the square.  Divide all terms by
-17 the coefficient of the squared term: 

Divide each side by '-17'.
-0.3529411765 + -0.1176470588x + x2 = 0

Move the constant term to the right:

Add '0.3529411765' to each side of the equation.
-0.3529411765 + -0.1176470588x + 0.3529411765 + x2 = 0 + 0.3529411765

Reorder the terms:
-0.3529411765 + 0.3529411765 + -0.1176470588x + x2 = 0 + 0.3529411765

Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000
0.0000000000 + -0.1176470588x + x2 = 0 + 0.3529411765
-0.1176470588x + x2 = 0 + 0.3529411765

Combine like terms: 0 + 0.3529411765 = 0.3529411765
-0.1176470588x + x2 = 0.3529411765

The x term is -0.1176470588x.  Take half its coefficient (-0.0588235294).
Square it (0.003460207611) and add it to both sides.

Add '0.003460207611' to each side of the equation.
-0.1176470588x + 0.003460207611 + x2 = 0.3529411765 + 0.003460207611

Reorder the terms:
0.003460207611 + -0.1176470588x + x2 = 0.3529411765 + 0.003460207611

Combine like terms: 0.3529411765 + 0.003460207611 = 0.356401384111
0.003460207611 + -0.1176470588x + x2 = 0.356401384111

Factor a perfect square on the left side:
(x + -0.0588235294)(x + -0.0588235294) = 0.356401384111

Calculate the square root of the right side: 0.596993622

Break this problem into two subproblems by setting 
(x + -0.0588235294) equal to 0.596993622 and -0.596993622.

Subproblem 1
x + -0.0588235294 = 0.596993622

Simplifying
x + -0.0588235294 = 0.596993622

Reorder the terms:
-0.0588235294 + x = 0.596993622

Solving
-0.0588235294 + x = 0.596993622

Solving for variable 'x'.

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

Add '0.0588235294' to each side of the equation.
-0.0588235294 + 0.0588235294 + x = 0.596993622 + 0.0588235294

Combine like terms: -0.0588235294 + 0.0588235294 = 0.0000000000
0.0000000000 + x = 0.596993622 + 0.0588235294
x = 0.596993622 + 0.0588235294

Combine like terms: 0.596993622 + 0.0588235294 = 0.6558171514
x = 0.6558171514

Simplifying
x = 0.6558171514

Subproblem 2
x + -0.0588235294 = -0.596993622

Simplifying
x + -0.0588235294 = -0.596993622

Reorder the terms:
-0.0588235294 + x = -0.596993622

Solving
-0.0588235294 + x = -0.596993622

Solving for variable 'x'.

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

Add '0.0588235294' to each side of the equation.
-0.0588235294 + 0.0588235294 + x = -0.596993622 + 0.0588235294

Combine like terms: -0.0588235294 + 0.0588235294 = 0.0000000000
0.0000000000 + x = -0.596993622 + 0.0588235294
x = -0.596993622 + 0.0588235294

Combine like terms: -0.596993622 + 0.0588235294 = -0.5381700926
x = -0.5381700926

Simplifying
x = -0.5381700926

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6558171514, -0.5381700926}