9x^2-8x-12=0

Solution for 9x^2-8x-12=0 equation:

Simplifying
9x2 + -8x + -12 = 0

Reorder the terms:
-12 + -8x + 9x2 = 0

Solving
-12 + -8x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-1.333333333 + -0.8888888889x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -0.8888888889x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -0.8888888889x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -0.8888888889x + x2 = 0 + 1.333333333
-0.8888888889x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-0.8888888889x + x2 = 1.333333333

The x term is -0.8888888889x.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889x + 0.1975308642 + x2 = 1.333333333 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889x + x2 = 1.333333333 + 0.1975308642

Combine like terms: 1.333333333 + 0.1975308642 = 1.5308641972
0.1975308642 + -0.8888888889x + x2 = 1.5308641972

Factor a perfect square on the left side:
(x + -0.4444444445)(x + -0.4444444445) = 1.5308641972

Calculate the square root of the right side: 1.237280969

Break this problem into two subproblems by setting 
(x + -0.4444444445) equal to 1.237280969 and -1.237280969.

Subproblem 1
x + -0.4444444445 = 1.237280969

Simplifying
x + -0.4444444445 = 1.237280969

Reorder the terms:
-0.4444444445 + x = 1.237280969

Solving
-0.4444444445 + x = 1.237280969

Solving for variable 'x'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + x = 1.237280969 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = 1.237280969 + 0.4444444445
x = 1.237280969 + 0.4444444445

Combine like terms: 1.237280969 + 0.4444444445 = 1.6817254135
x = 1.6817254135

Simplifying
x = 1.6817254135

Subproblem 2
x + -0.4444444445 = -1.237280969

Simplifying
x + -0.4444444445 = -1.237280969

Reorder the terms:
-0.4444444445 + x = -1.237280969

Solving
-0.4444444445 + x = -1.237280969

Solving for variable 'x'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + x = -1.237280969 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = -1.237280969 + 0.4444444445
x = -1.237280969 + 0.4444444445

Combine like terms: -1.237280969 + 0.4444444445 = -0.7928365245
x = -0.7928365245

Simplifying
x = -0.7928365245

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6817254135, -0.7928365245}