9x^2+24x-16=0

Solution for 9x^2+24x-16=0 equation:

Simplifying
9x2 + 24x + -16 = 0

Reorder the terms:
-16 + 24x + 9x2 = 0

Solving
-16 + 24x + 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'.
-1.777777778 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + 2.666666667x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + 2.666666667x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + 1.777777778
2.666666667x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
2.666666667x + x2 = 1.777777778

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 1.777777778 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 1.777777778 + 1.777777780

Combine like terms: 1.777777778 + 1.777777780 = 3.555555558
1.777777780 + 2.666666667x + x2 = 3.555555558

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 3.555555558

Calculate the square root of the right side: 1.885618084

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 1.885618084 and -1.885618084.

Subproblem 1
x + 1.333333334 = 1.885618084

Simplifying
x + 1.333333334 = 1.885618084

Reorder the terms:
1.333333334 + x = 1.885618084

Solving
1.333333334 + x = 1.885618084

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 1.885618084 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 1.885618084 + -1.333333334
x = 1.885618084 + -1.333333334

Combine like terms: 1.885618084 + -1.333333334 = 0.55228475
x = 0.55228475

Simplifying
x = 0.55228475

Subproblem 2
x + 1.333333334 = -1.885618084

Simplifying
x + 1.333333334 = -1.885618084

Reorder the terms:
1.333333334 + x = -1.885618084

Solving
1.333333334 + x = -1.885618084

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -1.885618084 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -1.885618084 + -1.333333334
x = -1.885618084 + -1.333333334

Combine like terms: -1.885618084 + -1.333333334 = -3.218951418
x = -3.218951418

Simplifying
x = -3.218951418

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.55228475, -3.218951418}