9n^2-18n-86=0

Solution for 9n^2-18n-86=0 equation:

Simplifying
9n2 + -18n + -86 = 0

Reorder the terms:
-86 + -18n + 9n2 = 0

Solving
-86 + -18n + 9n2 = 0

Solving for variable 'n'.

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

Divide each side by '9'.
-9.555555556 + -2n + n2 = 0

Move the constant term to the right:

Add '9.555555556' to each side of the equation.
-9.555555556 + -2n + 9.555555556 + n2 = 0 + 9.555555556

Reorder the terms:
-9.555555556 + 9.555555556 + -2n + n2 = 0 + 9.555555556

Combine like terms: -9.555555556 + 9.555555556 = 0.000000000
0.000000000 + -2n + n2 = 0 + 9.555555556
-2n + n2 = 0 + 9.555555556

Combine like terms: 0 + 9.555555556 = 9.555555556
-2n + n2 = 9.555555556

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 = 9.555555556 + 1

Reorder the terms:
1 + -2n + n2 = 9.555555556 + 1

Combine like terms: 9.555555556 + 1 = 10.555555556
1 + -2n + n2 = 10.555555556

Factor a perfect square on the left side:
(n + -1)(n + -1) = 10.555555556

Calculate the square root of the right side: 3.248931448

Break this problem into two subproblems by setting 
(n + -1) equal to 3.248931448 and -3.248931448.

Subproblem 1
n + -1 = 3.248931448

Simplifying
n + -1 = 3.248931448

Reorder the terms:
-1 + n = 3.248931448

Solving
-1 + n = 3.248931448

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 = 3.248931448 + 1

Combine like terms: -1 + 1 = 0
0 + n = 3.248931448 + 1
n = 3.248931448 + 1

Combine like terms: 3.248931448 + 1 = 4.248931448
n = 4.248931448

Simplifying
n = 4.248931448

Subproblem 2
n + -1 = -3.248931448

Simplifying
n + -1 = -3.248931448

Reorder the terms:
-1 + n = -3.248931448

Solving
-1 + n = -3.248931448

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 = -3.248931448 + 1

Combine like terms: -1 + 1 = 0
0 + n = -3.248931448 + 1
n = -3.248931448 + 1

Combine like terms: -3.248931448 + 1 = -2.248931448
n = -2.248931448

Simplifying
n = -2.248931448

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.248931448, -2.248931448}