0=6x^2+22x-4

Solution for 0=6x^2+22x-4 equation:

Simplifying
0 = 6x2 + 22x + -4

Reorder the terms:
0 = -4 + 22x + 6x2

Solving
0 = -4 + 22x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 4 = 4
4 + -22x + -6x2 = -4 + 22x + 6x2 + 4 + -22x + -6x2

Reorder the terms:
4 + -22x + -6x2 = -4 + 4 + 22x + -22x + 6x2 + -6x2

Combine like terms: -4 + 4 = 0
4 + -22x + -6x2 = 0 + 22x + -22x + 6x2 + -6x2
4 + -22x + -6x2 = 22x + -22x + 6x2 + -6x2

Combine like terms: 22x + -22x = 0
4 + -22x + -6x2 = 0 + 6x2 + -6x2
4 + -22x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
4 + -22x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -11x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -11x + -3x2)' equal to zero and attempt to solve:

Simplifying
2 + -11x + -3x2 = 0

Solving
2 + -11x + -3x2 = 0

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

Divide each side by '-3'.
-0.6666666667 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 3.666666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 3.666666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 3.666666667x + x2 = 0 + 0.6666666667
3.666666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
3.666666667x + x2 = 0.6666666667

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = 0.6666666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 0.6666666667 + 3.361111114

Combine like terms: 0.6666666667 + 3.361111114 = 4.0277777807
3.361111114 + 3.666666667x + x2 = 4.0277777807

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 4.0277777807

Calculate the square root of the right side: 2.006932431

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 2.006932431 and -2.006932431.

Subproblem 1
x + 1.833333334 = 2.006932431

Simplifying
x + 1.833333334 = 2.006932431

Reorder the terms:
1.833333334 + x = 2.006932431

Solving
1.833333334 + x = 2.006932431

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = 2.006932431 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 2.006932431 + -1.833333334
x = 2.006932431 + -1.833333334

Combine like terms: 2.006932431 + -1.833333334 = 0.173599097
x = 0.173599097

Simplifying
x = 0.173599097

Subproblem 2
x + 1.833333334 = -2.006932431

Simplifying
x + 1.833333334 = -2.006932431

Reorder the terms:
1.833333334 + x = -2.006932431

Solving
1.833333334 + x = -2.006932431

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = -2.006932431 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -2.006932431 + -1.833333334
x = -2.006932431 + -1.833333334

Combine like terms: -2.006932431 + -1.833333334 = -3.840265765
x = -3.840265765

Simplifying
x = -3.840265765

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.173599097, -3.840265765}
Solution
x = {0.173599097, -3.840265765}