0=46x^2-12-14x

Solution for 0=46x^2-12-14x equation:

Simplifying
0 = 46x2 + -12 + -14x

Reorder the terms:
0 = -12 + -14x + 46x2

Solving
0 = -12 + -14x + 46x2

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + 14x + -46x2 = -12 + -14x + 46x2 + 12 + 14x + -46x2

Reorder the terms:
12 + 14x + -46x2 = -12 + 12 + -14x + 14x + 46x2 + -46x2

Combine like terms: -12 + 12 = 0
12 + 14x + -46x2 = 0 + -14x + 14x + 46x2 + -46x2
12 + 14x + -46x2 = -14x + 14x + 46x2 + -46x2

Combine like terms: -14x + 14x = 0
12 + 14x + -46x2 = 0 + 46x2 + -46x2
12 + 14x + -46x2 = 46x2 + -46x2

Combine like terms: 46x2 + -46x2 = 0
12 + 14x + -46x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 7x + -23x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 7x + -23x2)' equal to zero and attempt to solve:

Simplifying
6 + 7x + -23x2 = 0

Solving
6 + 7x + -23x2 = 0

Begin completing the square.  Divide all terms by
-23 the coefficient of the squared term: 

Divide each side by '-23'.
-0.2608695652 + -0.3043478261x + x2 = 0

Move the constant term to the right:

Add '0.2608695652' to each side of the equation.
-0.2608695652 + -0.3043478261x + 0.2608695652 + x2 = 0 + 0.2608695652

Reorder the terms:
-0.2608695652 + 0.2608695652 + -0.3043478261x + x2 = 0 + 0.2608695652

Combine like terms: -0.2608695652 + 0.2608695652 = 0.0000000000
0.0000000000 + -0.3043478261x + x2 = 0 + 0.2608695652
-0.3043478261x + x2 = 0 + 0.2608695652

Combine like terms: 0 + 0.2608695652 = 0.2608695652
-0.3043478261x + x2 = 0.2608695652

The x term is -0.3043478261x.  Take half its coefficient (-0.1521739131).
Square it (0.02315689983) and add it to both sides.

Add '0.02315689983' to each side of the equation.
-0.3043478261x + 0.02315689983 + x2 = 0.2608695652 + 0.02315689983

Reorder the terms:
0.02315689983 + -0.3043478261x + x2 = 0.2608695652 + 0.02315689983

Combine like terms: 0.2608695652 + 0.02315689983 = 0.28402646503
0.02315689983 + -0.3043478261x + x2 = 0.28402646503

Factor a perfect square on the left side:
(x + -0.1521739131)(x + -0.1521739131) = 0.28402646503

Calculate the square root of the right side: 0.532941334

Break this problem into two subproblems by setting 
(x + -0.1521739131) equal to 0.532941334 and -0.532941334.

Subproblem 1
x + -0.1521739131 = 0.532941334

Simplifying
x + -0.1521739131 = 0.532941334

Reorder the terms:
-0.1521739131 + x = 0.532941334

Solving
-0.1521739131 + x = 0.532941334

Solving for variable 'x'.

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

Add '0.1521739131' to each side of the equation.
-0.1521739131 + 0.1521739131 + x = 0.532941334 + 0.1521739131

Combine like terms: -0.1521739131 + 0.1521739131 = 0.0000000000
0.0000000000 + x = 0.532941334 + 0.1521739131
x = 0.532941334 + 0.1521739131

Combine like terms: 0.532941334 + 0.1521739131 = 0.6851152471
x = 0.6851152471

Simplifying
x = 0.6851152471

Subproblem 2
x + -0.1521739131 = -0.532941334

Simplifying
x + -0.1521739131 = -0.532941334

Reorder the terms:
-0.1521739131 + x = -0.532941334

Solving
-0.1521739131 + x = -0.532941334

Solving for variable 'x'.

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

Add '0.1521739131' to each side of the equation.
-0.1521739131 + 0.1521739131 + x = -0.532941334 + 0.1521739131

Combine like terms: -0.1521739131 + 0.1521739131 = 0.0000000000
0.0000000000 + x = -0.532941334 + 0.1521739131
x = -0.532941334 + 0.1521739131

Combine like terms: -0.532941334 + 0.1521739131 = -0.3807674209
x = -0.3807674209

Simplifying
x = -0.3807674209

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6851152471, -0.3807674209}
Solution
x = {0.6851152471, -0.3807674209}