9x^2+8x-39=0

Solution for 9x^2+8x-39=0 equation:

Simplifying
9x2 + 8x + -39 = 0

Reorder the terms:
-39 + 8x + 9x2 = 0

Solving
-39 + 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'.
-4.333333333 + 0.8888888889x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + 0.8888888889x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + 0.8888888889x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + 0.8888888889x + x2 = 0 + 4.333333333
0.8888888889x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
0.8888888889x + x2 = 4.333333333

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 = 4.333333333 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889x + x2 = 4.333333333 + 0.1975308642

Combine like terms: 4.333333333 + 0.1975308642 = 4.5308641972
0.1975308642 + 0.8888888889x + x2 = 4.5308641972

Factor a perfect square on the left side:
(x + 0.4444444445)(x + 0.4444444445) = 4.5308641972

Calculate the square root of the right side: 2.128582673

Break this problem into two subproblems by setting 
(x + 0.4444444445) equal to 2.128582673 and -2.128582673.

Subproblem 1
x + 0.4444444445 = 2.128582673

Simplifying
x + 0.4444444445 = 2.128582673

Reorder the terms:
0.4444444445 + x = 2.128582673

Solving
0.4444444445 + x = 2.128582673

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 = 2.128582673 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = 2.128582673 + -0.4444444445
x = 2.128582673 + -0.4444444445

Combine like terms: 2.128582673 + -0.4444444445 = 1.6841382285
x = 1.6841382285

Simplifying
x = 1.6841382285

Subproblem 2
x + 0.4444444445 = -2.128582673

Simplifying
x + 0.4444444445 = -2.128582673

Reorder the terms:
0.4444444445 + x = -2.128582673

Solving
0.4444444445 + x = -2.128582673

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 = -2.128582673 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = -2.128582673 + -0.4444444445
x = -2.128582673 + -0.4444444445

Combine like terms: -2.128582673 + -0.4444444445 = -2.5730271175
x = -2.5730271175

Simplifying
x = -2.5730271175

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6841382285, -2.5730271175}