3x^2-40x+80=0

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Solution for 3x^2-40x+80=0 equation: 


Simplifying
3x2 + -40x + 80 = 0

Reorder the terms:
80 + -40x + 3x2 = 0

Solving
80 + -40x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
26.66666667 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '-26.66666667' to each side of the equation.
26.66666667 + -13.33333333x + -26.66666667 + x2 = 0 + -26.66666667

Reorder the terms:
26.66666667 + -26.66666667 + -13.33333333x + x2 = 0 + -26.66666667

Combine like terms: 26.66666667 + -26.66666667 = 0.00000000
0.00000000 + -13.33333333x + x2 = 0 + -26.66666667
-13.33333333x + x2 = 0 + -26.66666667

Combine like terms: 0 + -26.66666667 = -26.66666667
-13.33333333x + x2 = -26.66666667

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 = -26.66666667 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = -26.66666667 + 44.44444442

Combine like terms: -26.66666667 + 44.44444442 = 17.77777775
44.44444442 + -13.33333333x + x2 = 17.77777775

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 17.77777775

Calculate the square root of the right side: 4.21637021

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 4.21637021 and -4.21637021.


Subproblem 1
x + -6.666666665 = 4.21637021

Simplifying
x + -6.666666665 = 4.21637021

Reorder the terms:
-6.666666665 + x = 4.21637021

Solving
-6.666666665 + x = 4.21637021

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 = 4.21637021 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 4.21637021 + 6.666666665
x = 4.21637021 + 6.666666665

Combine like terms: 4.21637021 + 6.666666665 = 10.883036875
x = 10.883036875

Simplifying
x = 10.883036875


Subproblem 2
x + -6.666666665 = -4.21637021

Simplifying
x + -6.666666665 = -4.21637021

Reorder the terms:
-6.666666665 + x = -4.21637021

Solving
-6.666666665 + x = -4.21637021

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 = -4.21637021 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -4.21637021 + 6.666666665
x = -4.21637021 + 6.666666665

Combine like terms: -4.21637021 + 6.666666665 = 2.450296455
x = 2.450296455

Simplifying
x = 2.450296455


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.883036875, 2.450296455}

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