8*n^2-4*n=18

Solution for 8*n^2-4*n=18 equation:

Simplifying
8n2 + -4n = 18

Reorder the terms:
-4n + 8n2 = 18

Solving
-4n + 8n2 = 18

Solving for variable 'n'.

Reorder the terms:
-18 + -4n + 8n2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -4n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -2n + 4n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2n + 4n2)' equal to zero and attempt to solve:

Simplifying
-9 + -2n + 4n2 = 0

Solving
-9 + -2n + 4n2 = 0

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

Divide each side by '4'.
-2.25 + -0.5n + n2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -0.5n + 2.25 + n2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -0.5n + n2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -0.5n + n2 = 0 + 2.25
-0.5n + n2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-0.5n + n2 = 2.25

The n term is -0.5n.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5n + 0.0625 + n2 = 2.25 + 0.0625

Reorder the terms:
0.0625 + -0.5n + n2 = 2.25 + 0.0625

Combine like terms: 2.25 + 0.0625 = 2.3125
0.0625 + -0.5n + n2 = 2.3125

Factor a perfect square on the left side:
(n + -0.25)(n + -0.25) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(n + -0.25) equal to 1.520690633 and -1.520690633.

Subproblem 1
n + -0.25 = 1.520690633

Simplifying
n + -0.25 = 1.520690633

Reorder the terms:
-0.25 + n = 1.520690633

Solving
-0.25 + n = 1.520690633

Solving for variable 'n'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + n = 1.520690633 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = 1.520690633 + 0.25
n = 1.520690633 + 0.25

Combine like terms: 1.520690633 + 0.25 = 1.770690633
n = 1.770690633

Simplifying
n = 1.770690633

Subproblem 2
n + -0.25 = -1.520690633

Simplifying
n + -0.25 = -1.520690633

Reorder the terms:
-0.25 + n = -1.520690633

Solving
-0.25 + n = -1.520690633

Solving for variable 'n'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + n = -1.520690633 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = -1.520690633 + 0.25
n = -1.520690633 + 0.25

Combine like terms: -1.520690633 + 0.25 = -1.270690633
n = -1.270690633

Simplifying
n = -1.270690633

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.770690633, -1.270690633}
Solution
n = {1.770690633, -1.270690633}