3x^2-17x+6=0

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Solution for 3x^2-17x+6=0 equation: 


Simplifying
3x2 + -17x + 6 = 0

Reorder the terms:
6 + -17x + 3x2 = 0

Solving
6 + -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'.
2 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -5.666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -5.666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5.666666667x + x2 = 0 + -2
-5.666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5.666666667x + x2 = -2

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 = -2 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = -2 + 8.027777782

Combine like terms: -2 + 8.027777782 = 6.027777782
8.027777782 + -5.666666667x + x2 = 6.027777782

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 6.027777782

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 2.455153311 and -2.455153311.


Subproblem 1
x + -2.833333334 = 2.455153311

Simplifying
x + -2.833333334 = 2.455153311

Reorder the terms:
-2.833333334 + x = 2.455153311

Solving
-2.833333334 + x = 2.455153311

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 = 2.455153311 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 2.455153311 + 2.833333334
x = 2.455153311 + 2.833333334

Combine like terms: 2.455153311 + 2.833333334 = 5.288486645
x = 5.288486645

Simplifying
x = 5.288486645


Subproblem 2
x + -2.833333334 = -2.455153311

Simplifying
x + -2.833333334 = -2.455153311

Reorder the terms:
-2.833333334 + x = -2.455153311

Solving
-2.833333334 + x = -2.455153311

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 = -2.455153311 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -2.455153311 + 2.833333334
x = -2.455153311 + 2.833333334

Combine like terms: -2.455153311 + 2.833333334 = 0.378180023
x = 0.378180023

Simplifying
x = 0.378180023


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.288486645, 0.378180023}

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