3x^2-17x+12=0

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Solution for 3x^2-17x+12=0 equation: 


Simplifying
3x2 + -17x + 12 = 0

Reorder the terms:
12 + -17x + 3x2 = 0

Solving
12 + -17x + 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'.
4 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -5.666666667x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -5.666666667x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5.666666667x + x2 = 0 + -4
-5.666666667x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5.666666667x + x2 = -4

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = -4 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = -4 + 8.027777782

Combine like terms: -4 + 8.027777782 = 4.027777782
8.027777782 + -5.666666667x + x2 = 4.027777782

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 4.027777782

Calculate the square root of the right side: 2.006932431

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 2.006932431 and -2.006932431.


Subproblem 1
x + -2.833333334 = 2.006932431

Simplifying
x + -2.833333334 = 2.006932431

Reorder the terms:
-2.833333334 + x = 2.006932431

Solving
-2.833333334 + x = 2.006932431

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 2.006932431 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 2.006932431 + 2.833333334
x = 2.006932431 + 2.833333334

Combine like terms: 2.006932431 + 2.833333334 = 4.840265765
x = 4.840265765

Simplifying
x = 4.840265765


Subproblem 2
x + -2.833333334 = -2.006932431

Simplifying
x + -2.833333334 = -2.006932431

Reorder the terms:
-2.833333334 + x = -2.006932431

Solving
-2.833333334 + x = -2.006932431

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -2.006932431 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -2.006932431 + 2.833333334
x = -2.006932431 + 2.833333334

Combine like terms: -2.006932431 + 2.833333334 = 0.826400903
x = 0.826400903

Simplifying
x = 0.826400903


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.840265765, 0.826400903}

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