4880=4n^2+2n

Solution for 4880=4n^2+2n equation:

Simplifying
4880 = 4n2 + 2n

Reorder the terms:
4880 = 2n + 4n2

Solving
4880 = 2n + 4n2

Solving for variable 'n'.

Reorder the terms:
4880 + -2n + -4n2 = 2n + -2n + 4n2 + -4n2

Combine like terms: 2n + -2n = 0
4880 + -2n + -4n2 = 0 + 4n2 + -4n2
4880 + -2n + -4n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
4880 + -2n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2440 + -1n + -2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2440 + -1n + -2n2)' equal to zero and attempt to solve:

Simplifying
2440 + -1n + -2n2 = 0

Solving
2440 + -1n + -2n2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1220 + 0.5n + n2 = 0

Move the constant term to the right:

Add '1220' to each side of the equation.
-1220 + 0.5n + 1220 + n2 = 0 + 1220

Reorder the terms:
-1220 + 1220 + 0.5n + n2 = 0 + 1220

Combine like terms: -1220 + 1220 = 0
0 + 0.5n + n2 = 0 + 1220
0.5n + n2 = 0 + 1220

Combine like terms: 0 + 1220 = 1220
0.5n + n2 = 1220

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 = 1220 + 0.0625

Reorder the terms:
0.0625 + 0.5n + n2 = 1220 + 0.0625

Combine like terms: 1220 + 0.0625 = 1220.0625
0.0625 + 0.5n + n2 = 1220.0625

Factor a perfect square on the left side:
(n + 0.25)(n + 0.25) = 1220.0625

Calculate the square root of the right side: 34.929393067

Break this problem into two subproblems by setting 
(n + 0.25) equal to 34.929393067 and -34.929393067.

Subproblem 1
n + 0.25 = 34.929393067

Simplifying
n + 0.25 = 34.929393067

Reorder the terms:
0.25 + n = 34.929393067

Solving
0.25 + n = 34.929393067

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 = 34.929393067 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + n = 34.929393067 + -0.25
n = 34.929393067 + -0.25

Combine like terms: 34.929393067 + -0.25 = 34.679393067
n = 34.679393067

Simplifying
n = 34.679393067

Subproblem 2
n + 0.25 = -34.929393067

Simplifying
n + 0.25 = -34.929393067

Reorder the terms:
0.25 + n = -34.929393067

Solving
0.25 + n = -34.929393067

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 = -34.929393067 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + n = -34.929393067 + -0.25
n = -34.929393067 + -0.25

Combine like terms: -34.929393067 + -0.25 = -35.179393067
n = -35.179393067

Simplifying
n = -35.179393067

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {34.679393067, -35.179393067}
Solution
n = {34.679393067, -35.179393067}