9n^2-18n-17=0

Solution for 9n^2-18n-17=0 equation:

Simplifying
9n2 + -18n + -17 = 0

Reorder the terms:
-17 + -18n + 9n2 = 0

Solving
-17 + -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'.
-1.888888889 + -2n + n2 = 0

Move the constant term to the right:

Add '1.888888889' to each side of the equation.
-1.888888889 + -2n + 1.888888889 + n2 = 0 + 1.888888889

Reorder the terms:
-1.888888889 + 1.888888889 + -2n + n2 = 0 + 1.888888889

Combine like terms: -1.888888889 + 1.888888889 = 0.000000000
0.000000000 + -2n + n2 = 0 + 1.888888889
-2n + n2 = 0 + 1.888888889

Combine like terms: 0 + 1.888888889 = 1.888888889
-2n + n2 = 1.888888889

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 = 1.888888889 + 1

Reorder the terms:
1 + -2n + n2 = 1.888888889 + 1

Combine like terms: 1.888888889 + 1 = 2.888888889
1 + -2n + n2 = 2.888888889

Factor a perfect square on the left side:
(n + -1)(n + -1) = 2.888888889

Calculate the square root of the right side: 1.699673171

Break this problem into two subproblems by setting 
(n + -1) equal to 1.699673171 and -1.699673171.

Subproblem 1
n + -1 = 1.699673171

Simplifying
n + -1 = 1.699673171

Reorder the terms:
-1 + n = 1.699673171

Solving
-1 + n = 1.699673171

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 = 1.699673171 + 1

Combine like terms: -1 + 1 = 0
0 + n = 1.699673171 + 1
n = 1.699673171 + 1

Combine like terms: 1.699673171 + 1 = 2.699673171
n = 2.699673171

Simplifying
n = 2.699673171

Subproblem 2
n + -1 = -1.699673171

Simplifying
n + -1 = -1.699673171

Reorder the terms:
-1 + n = -1.699673171

Solving
-1 + n = -1.699673171

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 = -1.699673171 + 1

Combine like terms: -1 + 1 = 0
0 + n = -1.699673171 + 1
n = -1.699673171 + 1

Combine like terms: -1.699673171 + 1 = -0.699673171
n = -0.699673171

Simplifying
n = -0.699673171

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.699673171, -0.699673171}