5n^2-6n-1=0

Solution for 5n^2-6n-1=0 equation:

Simplifying
5n2 + -6n + -1 = 0

Reorder the terms:
-1 + -6n + 5n2 = 0

Solving
-1 + -6n + 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'.
-0.2 + -1.2n + n2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -1.2n + 0.2 + n2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -1.2n + n2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -1.2n + n2 = 0 + 0.2
-1.2n + n2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-1.2n + n2 = 0.2

The n term is -1.2n.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2n + 0.36 + n2 = 0.2 + 0.36

Reorder the terms:
0.36 + -1.2n + n2 = 0.2 + 0.36

Combine like terms: 0.2 + 0.36 = 0.56
0.36 + -1.2n + n2 = 0.56

Factor a perfect square on the left side:
(n + -0.6)(n + -0.6) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(n + -0.6) equal to 0.748331477 and -0.748331477.

Subproblem 1
n + -0.6 = 0.748331477

Simplifying
n + -0.6 = 0.748331477

Reorder the terms:
-0.6 + n = 0.748331477

Solving
-0.6 + n = 0.748331477

Solving for variable 'n'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + n = 0.748331477 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + n = 0.748331477 + 0.6
n = 0.748331477 + 0.6

Combine like terms: 0.748331477 + 0.6 = 1.348331477
n = 1.348331477

Simplifying
n = 1.348331477

Subproblem 2
n + -0.6 = -0.748331477

Simplifying
n + -0.6 = -0.748331477

Reorder the terms:
-0.6 + n = -0.748331477

Solving
-0.6 + n = -0.748331477

Solving for variable 'n'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + n = -0.748331477 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + n = -0.748331477 + 0.6
n = -0.748331477 + 0.6

Combine like terms: -0.748331477 + 0.6 = -0.148331477
n = -0.148331477

Simplifying
n = -0.148331477

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.348331477, -0.148331477}