6x^2-80x+240=0

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Solution for 6x^2-80x+240=0 equation: 


Simplifying
6x2 + -80x + 240 = 0

Reorder the terms:
240 + -80x + 6x2 = 0

Solving
240 + -80x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(120 + -40x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(120 + -40x + 3x2)' equal to zero and attempt to solve:

Simplifying
120 + -40x + 3x2 = 0

Solving
120 + -40x + 3x2 = 0

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

Divide each side by '3'.
40 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -13.33333333x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + -13.33333333x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -13.33333333x + x2 = 0 + -40
-13.33333333x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
-13.33333333x + x2 = -40

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = -40 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = -40 + 44.44444442

Combine like terms: -40 + 44.44444442 = 4.44444442
44.44444442 + -13.33333333x + x2 = 4.44444442

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 4.44444442

Calculate the square root of the right side: 2.108185101

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 2.108185101 and -2.108185101.


Subproblem 1
x + -6.666666665 = 2.108185101

Simplifying
x + -6.666666665 = 2.108185101

Reorder the terms:
-6.666666665 + x = 2.108185101

Solving
-6.666666665 + x = 2.108185101

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 2.108185101 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 2.108185101 + 6.666666665
x = 2.108185101 + 6.666666665

Combine like terms: 2.108185101 + 6.666666665 = 8.774851766
x = 8.774851766

Simplifying
x = 8.774851766


Subproblem 2
x + -6.666666665 = -2.108185101

Simplifying
x + -6.666666665 = -2.108185101

Reorder the terms:
-6.666666665 + x = -2.108185101

Solving
-6.666666665 + x = -2.108185101

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -2.108185101 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -2.108185101 + 6.666666665
x = -2.108185101 + 6.666666665

Combine like terms: -2.108185101 + 6.666666665 = 4.558481564
x = 4.558481564

Simplifying
x = 4.558481564


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.774851766, 4.558481564}
Solution
x = {8.774851766, 4.558481564}

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