9n^2+2n-30=0

Solution for 9n^2+2n-30=0 equation:

Simplifying
9n2 + 2n + -30 = 0

Reorder the terms:
-30 + 2n + 9n2 = 0

Solving
-30 + 2n + 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'.
-3.333333333 + 0.2222222222n + n2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 0.2222222222n + 3.333333333 + n2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 0.2222222222n + n2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 0.2222222222n + n2 = 0 + 3.333333333
0.2222222222n + n2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
0.2222222222n + n2 = 3.333333333

The n term is 0.2222222222n.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222n + 0.01234567901 + n2 = 3.333333333 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222n + n2 = 3.333333333 + 0.01234567901

Combine like terms: 3.333333333 + 0.01234567901 = 3.34567901201
0.01234567901 + 0.2222222222n + n2 = 3.34567901201

Factor a perfect square on the left side:
(n + 0.1111111111)(n + 0.1111111111) = 3.34567901201

Calculate the square root of the right side: 1.829119737

Break this problem into two subproblems by setting 
(n + 0.1111111111) equal to 1.829119737 and -1.829119737.

Subproblem 1
n + 0.1111111111 = 1.829119737

Simplifying
n + 0.1111111111 = 1.829119737

Reorder the terms:
0.1111111111 + n = 1.829119737

Solving
0.1111111111 + n = 1.829119737

Solving for variable 'n'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + n = 1.829119737 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + n = 1.829119737 + -0.1111111111
n = 1.829119737 + -0.1111111111

Combine like terms: 1.829119737 + -0.1111111111 = 1.7180086259
n = 1.7180086259

Simplifying
n = 1.7180086259

Subproblem 2
n + 0.1111111111 = -1.829119737

Simplifying
n + 0.1111111111 = -1.829119737

Reorder the terms:
0.1111111111 + n = -1.829119737

Solving
0.1111111111 + n = -1.829119737

Solving for variable 'n'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + n = -1.829119737 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + n = -1.829119737 + -0.1111111111
n = -1.829119737 + -0.1111111111

Combine like terms: -1.829119737 + -0.1111111111 = -1.9402308481
n = -1.9402308481

Simplifying
n = -1.9402308481

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.7180086259, -1.9402308481}