6n^2-11n+2=0

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Solution for 6n^2-11n+2=0 equation: 


Simplifying
6n2 + -11n + 2 = 0

Reorder the terms:
2 + -11n + 6n2 = 0

Solving
2 + -11n + 6n2 = 0

Solving for variable 'n'.

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

Divide each side by '6'.
0.3333333333 + -1.833333333n + n2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.833333333n + -0.3333333333 + n2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.833333333n + n2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.833333333n + n2 = 0 + -0.3333333333
-1.833333333n + n2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.833333333n + n2 = -0.3333333333

The n term is -1.833333333n.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333n + 0.8402777775 + n2 = -0.3333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333n + n2 = -0.3333333333 + 0.8402777775

Combine like terms: -0.3333333333 + 0.8402777775 = 0.5069444442
0.8402777775 + -1.833333333n + n2 = 0.5069444442

Factor a perfect square on the left side:
(n + -0.9166666665)(n + -0.9166666665) = 0.5069444442

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(n + -0.9166666665) equal to 0.712000312 and -0.712000312.


Subproblem 1
n + -0.9166666665 = 0.712000312

Simplifying
n + -0.9166666665 = 0.712000312

Reorder the terms:
-0.9166666665 + n = 0.712000312

Solving
-0.9166666665 + n = 0.712000312

Solving for variable 'n'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + n = 0.712000312 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + n = 0.712000312 + 0.9166666665
n = 0.712000312 + 0.9166666665

Combine like terms: 0.712000312 + 0.9166666665 = 1.6286669785
n = 1.6286669785

Simplifying
n = 1.6286669785


Subproblem 2
n + -0.9166666665 = -0.712000312

Simplifying
n + -0.9166666665 = -0.712000312

Reorder the terms:
-0.9166666665 + n = -0.712000312

Solving
-0.9166666665 + n = -0.712000312

Solving for variable 'n'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + n = -0.712000312 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + n = -0.712000312 + 0.9166666665
n = -0.712000312 + 0.9166666665

Combine like terms: -0.712000312 + 0.9166666665 = 0.2046663545
n = 0.2046663545

Simplifying
n = 0.2046663545


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.6286669785, 0.2046663545}

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