6x^2+4x-8=0

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Solution for 6x^2+4x-8=0 equation: 


Simplifying
6x2 + 4x + -8 = 0

Reorder the terms:
-8 + 4x + 6x2 = 0

Solving
-8 + 4x + 6x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 2x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 2x + 3x2 = 0

Solving
-4 + 2x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 0.6666666667x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 0.6666666667x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 1.333333333
0.6666666667x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
0.6666666667x + x2 = 1.333333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 1.333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 1.333333333 + 0.1111111112

Combine like terms: 1.333333333 + 0.1111111112 = 1.4444444442
0.1111111112 + 0.6666666667x + x2 = 1.4444444442

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 1.4444444442

Calculate the square root of the right side: 1.201850425

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.201850425 and -1.201850425.


Subproblem 1
x + 0.3333333334 = 1.201850425

Simplifying
x + 0.3333333334 = 1.201850425

Reorder the terms:
0.3333333334 + x = 1.201850425

Solving
0.3333333334 + x = 1.201850425

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 1.201850425 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 1.201850425 + -0.3333333334
x = 1.201850425 + -0.3333333334

Combine like terms: 1.201850425 + -0.3333333334 = 0.8685170916
x = 0.8685170916

Simplifying
x = 0.8685170916


Subproblem 2
x + 0.3333333334 = -1.201850425

Simplifying
x + 0.3333333334 = -1.201850425

Reorder the terms:
0.3333333334 + x = -1.201850425

Solving
0.3333333334 + x = -1.201850425

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -1.201850425 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -1.201850425 + -0.3333333334
x = -1.201850425 + -0.3333333334

Combine like terms: -1.201850425 + -0.3333333334 = -1.5351837584
x = -1.5351837584

Simplifying
x = -1.5351837584


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8685170916, -1.5351837584}
Solution
x = {0.8685170916, -1.5351837584}

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