11n^2-6n-34=8n^2

Solution for 11n^2-6n-34=8n^2 equation:

Simplifying
11n2 + -6n + -34 = 8n2

Reorder the terms:
-34 + -6n + 11n2 = 8n2

Solving
-34 + -6n + 11n2 = 8n2

Solving for variable 'n'.

Combine like terms: 11n2 + -8n2 = 3n2
-34 + -6n + 3n2 = 8n2 + -8n2

Combine like terms: 8n2 + -8n2 = 0
-34 + -6n + 3n2 = 0

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

Divide each side by '3'.
-11.33333333 + -2n + n2 = 0

Move the constant term to the right:

Add '11.33333333' to each side of the equation.
-11.33333333 + -2n + 11.33333333 + n2 = 0 + 11.33333333

Reorder the terms:
-11.33333333 + 11.33333333 + -2n + n2 = 0 + 11.33333333

Combine like terms: -11.33333333 + 11.33333333 = 0.00000000
0.00000000 + -2n + n2 = 0 + 11.33333333
-2n + n2 = 0 + 11.33333333

Combine like terms: 0 + 11.33333333 = 11.33333333
-2n + n2 = 11.33333333

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 11.33333333 + 1

Reorder the terms:
1 + -2n + n2 = 11.33333333 + 1

Combine like terms: 11.33333333 + 1 = 12.33333333
1 + -2n + n2 = 12.33333333

Factor a perfect square on the left side:
(n + -1)(n + -1) = 12.33333333

Calculate the square root of the right side: 3.511884584

Break this problem into two subproblems by setting 
(n + -1) equal to 3.511884584 and -3.511884584.

Subproblem 1
n + -1 = 3.511884584

Simplifying
n + -1 = 3.511884584

Reorder the terms:
-1 + n = 3.511884584

Solving
-1 + n = 3.511884584

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = 3.511884584 + 1

Combine like terms: -1 + 1 = 0
0 + n = 3.511884584 + 1
n = 3.511884584 + 1

Combine like terms: 3.511884584 + 1 = 4.511884584
n = 4.511884584

Simplifying
n = 4.511884584

Subproblem 2
n + -1 = -3.511884584

Simplifying
n + -1 = -3.511884584

Reorder the terms:
-1 + n = -3.511884584

Solving
-1 + n = -3.511884584

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = -3.511884584 + 1

Combine like terms: -1 + 1 = 0
0 + n = -3.511884584 + 1
n = -3.511884584 + 1

Combine like terms: -3.511884584 + 1 = -2.511884584
n = -2.511884584

Simplifying
n = -2.511884584

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.511884584, -2.511884584}