-5n^2+5n+8=0

Solution for -5n^2+5n+8=0 equation:

Simplifying
-5n2 + 5n + 8 = 0

Reorder the terms:
8 + 5n + -5n2 = 0

Solving
8 + 5n + -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'.
-1.6 + -1n + n2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -1n + 1.6 + n2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -1n + n2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -1n + n2 = 0 + 1.6
-1n + n2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-1n + n2 = 1.6

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 1.6 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 1.6 + 0.25

Combine like terms: 1.6 + 0.25 = 1.85
0.25 + -1n + n2 = 1.85

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 1.85

Calculate the square root of the right side: 1.360147051

Break this problem into two subproblems by setting 
(n + -0.5) equal to 1.360147051 and -1.360147051.

Subproblem 1
n + -0.5 = 1.360147051

Simplifying
n + -0.5 = 1.360147051

Reorder the terms:
-0.5 + n = 1.360147051

Solving
-0.5 + n = 1.360147051

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 1.360147051 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 1.360147051 + 0.5
n = 1.360147051 + 0.5

Combine like terms: 1.360147051 + 0.5 = 1.860147051
n = 1.860147051

Simplifying
n = 1.860147051

Subproblem 2
n + -0.5 = -1.360147051

Simplifying
n + -0.5 = -1.360147051

Reorder the terms:
-0.5 + n = -1.360147051

Solving
-0.5 + n = -1.360147051

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -1.360147051 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -1.360147051 + 0.5
n = -1.360147051 + 0.5

Combine like terms: -1.360147051 + 0.5 = -0.860147051
n = -0.860147051

Simplifying
n = -0.860147051

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.860147051, -0.860147051}