8n^2+4n-14=0

Solution for 8n^2+4n-14=0 equation:

Simplifying
8n2 + 4n + -14 = 0

Reorder the terms:
-14 + 4n + 8n2 = 0

Solving
-14 + 4n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 2n + 4n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + 2n + 4n2)' equal to zero and attempt to solve:

Simplifying
-7 + 2n + 4n2 = 0

Solving
-7 + 2n + 4n2 = 0

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

Divide each side by '4'.
-1.75 + 0.5n + n2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 0.5n + 1.75 + n2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 0.5n + n2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 0.5n + n2 = 0 + 1.75
0.5n + n2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
0.5n + n2 = 1.75

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 = 1.75 + 0.0625

Reorder the terms:
0.0625 + 0.5n + n2 = 1.75 + 0.0625

Combine like terms: 1.75 + 0.0625 = 1.8125
0.0625 + 0.5n + n2 = 1.8125

Factor a perfect square on the left side:
(n + 0.25)(n + 0.25) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(n + 0.25) equal to 1.346291202 and -1.346291202.

Subproblem 1
n + 0.25 = 1.346291202

Simplifying
n + 0.25 = 1.346291202

Reorder the terms:
0.25 + n = 1.346291202

Solving
0.25 + n = 1.346291202

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 = 1.346291202 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + n = 1.346291202 + -0.25
n = 1.346291202 + -0.25

Combine like terms: 1.346291202 + -0.25 = 1.096291202
n = 1.096291202

Simplifying
n = 1.096291202

Subproblem 2
n + 0.25 = -1.346291202

Simplifying
n + 0.25 = -1.346291202

Reorder the terms:
0.25 + n = -1.346291202

Solving
0.25 + n = -1.346291202

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 = -1.346291202 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + n = -1.346291202 + -0.25
n = -1.346291202 + -0.25

Combine like terms: -1.346291202 + -0.25 = -1.596291202
n = -1.596291202

Simplifying
n = -1.596291202

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.096291202, -1.596291202}
Solution
n = {1.096291202, -1.596291202}