6x^2+8x-48=0

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Solution for 6x^2+8x-48=0 equation: 


Simplifying
6x2 + 8x + -48 = 0

Reorder the terms:
-48 + 8x + 6x2 = 0

Solving
-48 + 8x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + 4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-24 + 4x + 3x2 = 0

Solving
-24 + 4x + 3x2 = 0

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

Divide each side by '3'.
-8 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 1.333333333x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 1.333333333x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 1.333333333x + x2 = 0 + 8
1.333333333x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
1.333333333x + x2 = 8

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 8 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 8 + 0.4444444442

Combine like terms: 8 + 0.4444444442 = 8.4444444442
0.4444444442 + 1.333333333x + x2 = 8.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 8.4444444442

Calculate the square root of the right side: 2.905932629

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 2.905932629 and -2.905932629.


Subproblem 1
x + 0.6666666665 = 2.905932629

Simplifying
x + 0.6666666665 = 2.905932629

Reorder the terms:
0.6666666665 + x = 2.905932629

Solving
0.6666666665 + x = 2.905932629

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 2.905932629 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 2.905932629 + -0.6666666665
x = 2.905932629 + -0.6666666665

Combine like terms: 2.905932629 + -0.6666666665 = 2.2392659625
x = 2.2392659625

Simplifying
x = 2.2392659625


Subproblem 2
x + 0.6666666665 = -2.905932629

Simplifying
x + 0.6666666665 = -2.905932629

Reorder the terms:
0.6666666665 + x = -2.905932629

Solving
0.6666666665 + x = -2.905932629

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -2.905932629 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -2.905932629 + -0.6666666665
x = -2.905932629 + -0.6666666665

Combine like terms: -2.905932629 + -0.6666666665 = -3.5725992955
x = -3.5725992955

Simplifying
x = -3.5725992955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2392659625, -3.5725992955}
Solution
x = {2.2392659625, -3.5725992955}

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