-6n^2+10n+1=0

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Solution for -6n^2+10n+1=0 equation: 


Simplifying
-6n2 + 10n + 1 = 0

Reorder the terms:
1 + 10n + -6n2 = 0

Solving
1 + 10n + -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'.
-0.1666666667 + -1.666666667n + n2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -1.666666667n + 0.1666666667 + n2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -1.666666667n + n2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -1.666666667n + n2 = 0 + 0.1666666667
-1.666666667n + n2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-1.666666667n + n2 = 0.1666666667

The n term is -1.666666667n.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667n + 0.6944444447 + n2 = 0.1666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667n + n2 = 0.1666666667 + 0.6944444447

Combine like terms: 0.1666666667 + 0.6944444447 = 0.8611111114
0.6944444447 + -1.666666667n + n2 = 0.8611111114

Factor a perfect square on the left side:
(n + -0.8333333335)(n + -0.8333333335) = 0.8611111114

Calculate the square root of the right side: 0.927960727

Break this problem into two subproblems by setting 
(n + -0.8333333335) equal to 0.927960727 and -0.927960727.


Subproblem 1
n + -0.8333333335 = 0.927960727

Simplifying
n + -0.8333333335 = 0.927960727

Reorder the terms:
-0.8333333335 + n = 0.927960727

Solving
-0.8333333335 + n = 0.927960727

Solving for variable 'n'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + n = 0.927960727 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + n = 0.927960727 + 0.8333333335
n = 0.927960727 + 0.8333333335

Combine like terms: 0.927960727 + 0.8333333335 = 1.7612940605
n = 1.7612940605

Simplifying
n = 1.7612940605


Subproblem 2
n + -0.8333333335 = -0.927960727

Simplifying
n + -0.8333333335 = -0.927960727

Reorder the terms:
-0.8333333335 + n = -0.927960727

Solving
-0.8333333335 + n = -0.927960727

Solving for variable 'n'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + n = -0.927960727 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + n = -0.927960727 + 0.8333333335
n = -0.927960727 + 0.8333333335

Combine like terms: -0.927960727 + 0.8333333335 = -0.0946273935
n = -0.0946273935

Simplifying
n = -0.0946273935


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.7612940605, -0.0946273935}

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