5n^2+110n+6=0

Solution for 5n^2+110n+6=0 equation:

Simplifying
5n2 + 110n + 6 = 0

Reorder the terms:
6 + 110n + 5n2 = 0

Solving
6 + 110n + 5n2 = 0

Solving for variable 'n'.

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

Divide each side by '5'.
1.2 + 22n + n2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 22n + -1.2 + n2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 22n + n2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 22n + n2 = 0 + -1.2
22n + n2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
22n + n2 = -1.2

The n term is 22n.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22n + 121 + n2 = -1.2 + 121

Reorder the terms:
121 + 22n + n2 = -1.2 + 121

Combine like terms: -1.2 + 121 = 119.8
121 + 22n + n2 = 119.8

Factor a perfect square on the left side:
(n + 11)(n + 11) = 119.8

Calculate the square root of the right side: 10.945318634

Break this problem into two subproblems by setting 
(n + 11) equal to 10.945318634 and -10.945318634.

Subproblem 1
n + 11 = 10.945318634

Simplifying
n + 11 = 10.945318634

Reorder the terms:
11 + n = 10.945318634

Solving
11 + n = 10.945318634

Solving for variable 'n'.

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

Add '-11' to each side of the equation.
11 + -11 + n = 10.945318634 + -11

Combine like terms: 11 + -11 = 0
0 + n = 10.945318634 + -11
n = 10.945318634 + -11

Combine like terms: 10.945318634 + -11 = -0.054681366
n = -0.054681366

Simplifying
n = -0.054681366

Subproblem 2
n + 11 = -10.945318634

Simplifying
n + 11 = -10.945318634

Reorder the terms:
11 + n = -10.945318634

Solving
11 + n = -10.945318634

Solving for variable 'n'.

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

Add '-11' to each side of the equation.
11 + -11 + n = -10.945318634 + -11

Combine like terms: 11 + -11 = 0
0 + n = -10.945318634 + -11
n = -10.945318634 + -11

Combine like terms: -10.945318634 + -11 = -21.945318634
n = -21.945318634

Simplifying
n = -21.945318634

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.054681366, -21.945318634}