12x^2-80x+75=0

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Solution for 12x^2-80x+75=0 equation: 


Simplifying
12x2 + -80x + 75 = 0

Reorder the terms:
75 + -80x + 12x2 = 0

Solving
75 + -80x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
6.25 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + -6.666666667x + -6.25 + x2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + -6.666666667x + x2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + -6.666666667x + x2 = 0 + -6.25
-6.666666667x + x2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
-6.666666667x + x2 = -6.25

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -6.25 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -6.25 + 11.11111112

Combine like terms: -6.25 + 11.11111112 = 4.86111112
11.11111112 + -6.666666667x + x2 = 4.86111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 4.86111112

Calculate the square root of the right side: 2.204792761

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 2.204792761 and -2.204792761.


Subproblem 1
x + -3.333333334 = 2.204792761

Simplifying
x + -3.333333334 = 2.204792761

Reorder the terms:
-3.333333334 + x = 2.204792761

Solving
-3.333333334 + x = 2.204792761

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 2.204792761 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 2.204792761 + 3.333333334
x = 2.204792761 + 3.333333334

Combine like terms: 2.204792761 + 3.333333334 = 5.538126095
x = 5.538126095

Simplifying
x = 5.538126095


Subproblem 2
x + -3.333333334 = -2.204792761

Simplifying
x + -3.333333334 = -2.204792761

Reorder the terms:
-3.333333334 + x = -2.204792761

Solving
-3.333333334 + x = -2.204792761

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -2.204792761 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -2.204792761 + 3.333333334
x = -2.204792761 + 3.333333334

Combine like terms: -2.204792761 + 3.333333334 = 1.128540573
x = 1.128540573

Simplifying
x = 1.128540573


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.538126095, 1.128540573}

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