9n^2+18n-8=0

Solution for 9n^2+18n-8=0 equation:

Simplifying
9n2 + 18n + -8 = 0

Reorder the terms:
-8 + 18n + 9n2 = 0

Solving
-8 + 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'.
-0.8888888889 + 2n + n2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + 2n + 0.8888888889 + n2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + 2n + n2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + 2n + n2 = 0 + 0.8888888889
2n + n2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
2n + n2 = 0.8888888889

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 = 0.8888888889 + 1

Reorder the terms:
1 + 2n + n2 = 0.8888888889 + 1

Combine like terms: 0.8888888889 + 1 = 1.8888888889
1 + 2n + n2 = 1.8888888889

Factor a perfect square on the left side:
(n + 1)(n + 1) = 1.8888888889

Calculate the square root of the right side: 1.374368542

Break this problem into two subproblems by setting 
(n + 1) equal to 1.374368542 and -1.374368542.

Subproblem 1
n + 1 = 1.374368542

Simplifying
n + 1 = 1.374368542

Reorder the terms:
1 + n = 1.374368542

Solving
1 + n = 1.374368542

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 = 1.374368542 + -1

Combine like terms: 1 + -1 = 0
0 + n = 1.374368542 + -1
n = 1.374368542 + -1

Combine like terms: 1.374368542 + -1 = 0.374368542
n = 0.374368542

Simplifying
n = 0.374368542

Subproblem 2
n + 1 = -1.374368542

Simplifying
n + 1 = -1.374368542

Reorder the terms:
1 + n = -1.374368542

Solving
1 + n = -1.374368542

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 = -1.374368542 + -1

Combine like terms: 1 + -1 = 0
0 + n = -1.374368542 + -1
n = -1.374368542 + -1

Combine like terms: -1.374368542 + -1 = -2.374368542
n = -2.374368542

Simplifying
n = -2.374368542

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.374368542, -2.374368542}