3x^2-23x+6=0

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Solution for 3x^2-23x+6=0 equation: 


Simplifying
3x2 + -23x + 6 = 0

Reorder the terms:
6 + -23x + 3x2 = 0

Solving
6 + -23x + 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'.
2 + -7.666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -7.666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -7.666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7.666666667x + x2 = 0 + -2
-7.666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7.666666667x + x2 = -2

The x term is -7.666666667x.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667x + 14.69444445 + x2 = -2 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667x + x2 = -2 + 14.69444445

Combine like terms: -2 + 14.69444445 = 12.69444445
14.69444445 + -7.666666667x + x2 = 12.69444445

Factor a perfect square on the left side:
(x + -3.833333334)(x + -3.833333334) = 12.69444445

Calculate the square root of the right side: 3.562926389

Break this problem into two subproblems by setting 
(x + -3.833333334) equal to 3.562926389 and -3.562926389.


Subproblem 1
x + -3.833333334 = 3.562926389

Simplifying
x + -3.833333334 = 3.562926389

Reorder the terms:
-3.833333334 + x = 3.562926389

Solving
-3.833333334 + x = 3.562926389

Solving for variable 'x'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + x = 3.562926389 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + x = 3.562926389 + 3.833333334
x = 3.562926389 + 3.833333334

Combine like terms: 3.562926389 + 3.833333334 = 7.396259723
x = 7.396259723

Simplifying
x = 7.396259723


Subproblem 2
x + -3.833333334 = -3.562926389

Simplifying
x + -3.833333334 = -3.562926389

Reorder the terms:
-3.833333334 + x = -3.562926389

Solving
-3.833333334 + x = -3.562926389

Solving for variable 'x'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + x = -3.562926389 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + x = -3.562926389 + 3.833333334
x = -3.562926389 + 3.833333334

Combine like terms: -3.562926389 + 3.833333334 = 0.270406945
x = 0.270406945

Simplifying
x = 0.270406945


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.396259723, 0.270406945}

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