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

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

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

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

Combine like terms: 11x + -3x = 8x
0 = -6 + 8x + 3x2 + 14x2

Combine like terms: 3x2 + 14x2 = 17x2
0 = -6 + 8x + 17x2

Solving
0 = -6 + 8x + 17x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -8x + -17x2 = -6 + 8x + 17x2 + 6 + -8x + -17x2

Reorder the terms:
6 + -8x + -17x2 = -6 + 6 + 8x + -8x + 17x2 + -17x2

Combine like terms: -6 + 6 = 0
6 + -8x + -17x2 = 0 + 8x + -8x + 17x2 + -17x2
6 + -8x + -17x2 = 8x + -8x + 17x2 + -17x2

Combine like terms: 8x + -8x = 0
6 + -8x + -17x2 = 0 + 17x2 + -17x2
6 + -8x + -17x2 = 17x2 + -17x2

Combine like terms: 17x2 + -17x2 = 0
6 + -8x + -17x2 = 0

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

Divide each side by '-17'.
-0.3529411765 + 0.4705882353x + x2 = 0

Move the constant term to the right:

Add '0.3529411765' to each side of the equation.
-0.3529411765 + 0.4705882353x + 0.3529411765 + x2 = 0 + 0.3529411765

Reorder the terms:
-0.3529411765 + 0.3529411765 + 0.4705882353x + x2 = 0 + 0.3529411765

Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000
0.0000000000 + 0.4705882353x + x2 = 0 + 0.3529411765
0.4705882353x + x2 = 0 + 0.3529411765

Combine like terms: 0 + 0.3529411765 = 0.3529411765
0.4705882353x + x2 = 0.3529411765

The x term is 0.4705882353x.  Take half its coefficient (0.2352941177).
Square it (0.05536332182) and add it to both sides.

Add '0.05536332182' to each side of the equation.
0.4705882353x + 0.05536332182 + x2 = 0.3529411765 + 0.05536332182

Reorder the terms:
0.05536332182 + 0.4705882353x + x2 = 0.3529411765 + 0.05536332182

Combine like terms: 0.3529411765 + 0.05536332182 = 0.40830449832
0.05536332182 + 0.4705882353x + x2 = 0.40830449832

Factor a perfect square on the left side:
(x + 0.2352941177)(x + 0.2352941177) = 0.40830449832

Calculate the square root of the right side: 0.638987088

Break this problem into two subproblems by setting 
(x + 0.2352941177) equal to 0.638987088 and -0.638987088.

Subproblem 1
x + 0.2352941177 = 0.638987088

Simplifying
x + 0.2352941177 = 0.638987088

Reorder the terms:
0.2352941177 + x = 0.638987088

Solving
0.2352941177 + x = 0.638987088

Solving for variable 'x'.

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

Add '-0.2352941177' to each side of the equation.
0.2352941177 + -0.2352941177 + x = 0.638987088 + -0.2352941177

Combine like terms: 0.2352941177 + -0.2352941177 = 0.0000000000
0.0000000000 + x = 0.638987088 + -0.2352941177
x = 0.638987088 + -0.2352941177

Combine like terms: 0.638987088 + -0.2352941177 = 0.4036929703
x = 0.4036929703

Simplifying
x = 0.4036929703

Subproblem 2
x + 0.2352941177 = -0.638987088

Simplifying
x + 0.2352941177 = -0.638987088

Reorder the terms:
0.2352941177 + x = -0.638987088

Solving
0.2352941177 + x = -0.638987088

Solving for variable 'x'.

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

Add '-0.2352941177' to each side of the equation.
0.2352941177 + -0.2352941177 + x = -0.638987088 + -0.2352941177

Combine like terms: 0.2352941177 + -0.2352941177 = 0.0000000000
0.0000000000 + x = -0.638987088 + -0.2352941177
x = -0.638987088 + -0.2352941177

Combine like terms: -0.638987088 + -0.2352941177 = -0.8742812057
x = -0.8742812057

Simplifying
x = -0.8742812057

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4036929703, -0.8742812057}