6x^2-12+38x=0

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Solution for 6x^2-12+38x=0 equation: 


Simplifying
6x2 + -12 + 38x = 0

Reorder the terms:
-12 + 38x + 6x2 = 0

Solving
-12 + 38x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 19x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + 19x + 3x2)' equal to zero and attempt to solve:

Simplifying
-6 + 19x + 3x2 = 0

Solving
-6 + 19x + 3x2 = 0

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

Divide each side by '3'.
-2 + 6.333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 6.333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 6.333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 6.333333333x + x2 = 0 + 2
6.333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
6.333333333x + x2 = 2

The x term is 6.333333333x.  Take half its coefficient (3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
6.333333333x + 10.02777778 + x2 = 2 + 10.02777778

Reorder the terms:
10.02777778 + 6.333333333x + x2 = 2 + 10.02777778

Combine like terms: 2 + 10.02777778 = 12.02777778
10.02777778 + 6.333333333x + x2 = 12.02777778

Factor a perfect square on the left side:
(x + 3.166666667)(x + 3.166666667) = 12.02777778

Calculate the square root of the right side: 3.468108675

Break this problem into two subproblems by setting 
(x + 3.166666667) equal to 3.468108675 and -3.468108675.


Subproblem 1
x + 3.166666667 = 3.468108675

Simplifying
x + 3.166666667 = 3.468108675

Reorder the terms:
3.166666667 + x = 3.468108675

Solving
3.166666667 + x = 3.468108675

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = 3.468108675 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = 3.468108675 + -3.166666667
x = 3.468108675 + -3.166666667

Combine like terms: 3.468108675 + -3.166666667 = 0.301442008
x = 0.301442008

Simplifying
x = 0.301442008


Subproblem 2
x + 3.166666667 = -3.468108675

Simplifying
x + 3.166666667 = -3.468108675

Reorder the terms:
3.166666667 + x = -3.468108675

Solving
3.166666667 + x = -3.468108675

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = -3.468108675 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = -3.468108675 + -3.166666667
x = -3.468108675 + -3.166666667

Combine like terms: -3.468108675 + -3.166666667 = -6.634775342
x = -6.634775342

Simplifying
x = -6.634775342


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.301442008, -6.634775342}
Solution
x = {0.301442008, -6.634775342}

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