0=5n^2-2n-728

Solution for 0=5n^2-2n-728 equation:

Simplifying
0 = 5n2 + -2n + -728

Reorder the terms:
0 = -728 + -2n + 5n2

Solving
0 = -728 + -2n + 5n2

Solving for variable 'n'.

Combine like terms: 0 + 728 = 728
728 + 2n + -5n2 = -728 + -2n + 5n2 + 728 + 2n + -5n2

Reorder the terms:
728 + 2n + -5n2 = -728 + 728 + -2n + 2n + 5n2 + -5n2

Combine like terms: -728 + 728 = 0
728 + 2n + -5n2 = 0 + -2n + 2n + 5n2 + -5n2
728 + 2n + -5n2 = -2n + 2n + 5n2 + -5n2

Combine like terms: -2n + 2n = 0
728 + 2n + -5n2 = 0 + 5n2 + -5n2
728 + 2n + -5n2 = 5n2 + -5n2

Combine like terms: 5n2 + -5n2 = 0
728 + 2n + -5n2 = 0

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

Divide each side by '-5'.
-145.6 + -0.4n + n2 = 0

Move the constant term to the right:

Add '145.6' to each side of the equation.
-145.6 + -0.4n + 145.6 + n2 = 0 + 145.6

Reorder the terms:
-145.6 + 145.6 + -0.4n + n2 = 0 + 145.6

Combine like terms: -145.6 + 145.6 = 0.0
0.0 + -0.4n + n2 = 0 + 145.6
-0.4n + n2 = 0 + 145.6

Combine like terms: 0 + 145.6 = 145.6
-0.4n + n2 = 145.6

The n term is -0.4n.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4n + 0.04 + n2 = 145.6 + 0.04

Reorder the terms:
0.04 + -0.4n + n2 = 145.6 + 0.04

Combine like terms: 145.6 + 0.04 = 145.64
0.04 + -0.4n + n2 = 145.64

Factor a perfect square on the left side:
(n + -0.2)(n + -0.2) = 145.64

Calculate the square root of the right side: 12.068139873

Break this problem into two subproblems by setting 
(n + -0.2) equal to 12.068139873 and -12.068139873.

Subproblem 1
n + -0.2 = 12.068139873

Simplifying
n + -0.2 = 12.068139873

Reorder the terms:
-0.2 + n = 12.068139873

Solving
-0.2 + n = 12.068139873

Solving for variable 'n'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + n = 12.068139873 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + n = 12.068139873 + 0.2
n = 12.068139873 + 0.2

Combine like terms: 12.068139873 + 0.2 = 12.268139873
n = 12.268139873

Simplifying
n = 12.268139873

Subproblem 2
n + -0.2 = -12.068139873

Simplifying
n + -0.2 = -12.068139873

Reorder the terms:
-0.2 + n = -12.068139873

Solving
-0.2 + n = -12.068139873

Solving for variable 'n'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + n = -12.068139873 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + n = -12.068139873 + 0.2
n = -12.068139873 + 0.2

Combine like terms: -12.068139873 + 0.2 = -11.868139873
n = -11.868139873

Simplifying
n = -11.868139873

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {12.268139873, -11.868139873}