0=6x^2-18x-86

Solution for 0=6x^2-18x-86 equation:

Simplifying
0 = 6x2 + -18x + -86

Reorder the terms:
0 = -86 + -18x + 6x2

Solving
0 = -86 + -18x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 86 = 86
86 + 18x + -6x2 = -86 + -18x + 6x2 + 86 + 18x + -6x2

Reorder the terms:
86 + 18x + -6x2 = -86 + 86 + -18x + 18x + 6x2 + -6x2

Combine like terms: -86 + 86 = 0
86 + 18x + -6x2 = 0 + -18x + 18x + 6x2 + -6x2
86 + 18x + -6x2 = -18x + 18x + 6x2 + -6x2

Combine like terms: -18x + 18x = 0
86 + 18x + -6x2 = 0 + 6x2 + -6x2
86 + 18x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
86 + 18x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(43 + 9x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(43 + 9x + -3x2)' equal to zero and attempt to solve:

Simplifying
43 + 9x + -3x2 = 0

Solving
43 + 9x + -3x2 = 0

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

Divide each side by '-3'.
-14.33333333 + -3x + x2 = 0

Move the constant term to the right:

Add '14.33333333' to each side of the equation.
-14.33333333 + -3x + 14.33333333 + x2 = 0 + 14.33333333

Reorder the terms:
-14.33333333 + 14.33333333 + -3x + x2 = 0 + 14.33333333

Combine like terms: -14.33333333 + 14.33333333 = 0.00000000
0.00000000 + -3x + x2 = 0 + 14.33333333
-3x + x2 = 0 + 14.33333333

Combine like terms: 0 + 14.33333333 = 14.33333333
-3x + x2 = 14.33333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 14.33333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 14.33333333 + 2.25

Combine like terms: 14.33333333 + 2.25 = 16.58333333
2.25 + -3x + x2 = 16.58333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 16.58333333

Calculate the square root of the right side: 4.072263907

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.072263907 and -4.072263907.

Subproblem 1
x + -1.5 = 4.072263907

Simplifying
x + -1.5 = 4.072263907

Reorder the terms:
-1.5 + x = 4.072263907

Solving
-1.5 + x = 4.072263907

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 4.072263907 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.072263907 + 1.5
x = 4.072263907 + 1.5

Combine like terms: 4.072263907 + 1.5 = 5.572263907
x = 5.572263907

Simplifying
x = 5.572263907

Subproblem 2
x + -1.5 = -4.072263907

Simplifying
x + -1.5 = -4.072263907

Reorder the terms:
-1.5 + x = -4.072263907

Solving
-1.5 + x = -4.072263907

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -4.072263907 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.072263907 + 1.5
x = -4.072263907 + 1.5

Combine like terms: -4.072263907 + 1.5 = -2.572263907
x = -2.572263907

Simplifying
x = -2.572263907

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.572263907, -2.572263907}
Solution
x = {5.572263907, -2.572263907}