2n^2+4n-1=

Solution for 2n^2+4n-1= equation:

Simplifying
2n2 + 4n + -1 = 0

Reorder the terms:
-1 + 4n + 2n2 = 0

Solving
-1 + 4n + 2n2 = 0

Solving for variable 'n'.

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

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

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2n + 0.5 + n2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2n + n2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2n + n2 = 0 + 0.5
2n + n2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2n + n2 = 0.5

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 0.5 + 1

Reorder the terms:
1 + 2n + n2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + 2n + n2 = 1.5

Factor a perfect square on the left side:
(n + 1)(n + 1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(n + 1) equal to 1.224744871 and -1.224744871.

Subproblem 1
n + 1 = 1.224744871

Simplifying
n + 1 = 1.224744871

Reorder the terms:
1 + n = 1.224744871

Solving
1 + n = 1.224744871

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + n = 1.224744871 + -1
n = 1.224744871 + -1

Combine like terms: 1.224744871 + -1 = 0.224744871
n = 0.224744871

Simplifying
n = 0.224744871

Subproblem 2
n + 1 = -1.224744871

Simplifying
n + 1 = -1.224744871

Reorder the terms:
1 + n = -1.224744871

Solving
1 + n = -1.224744871

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + n = -1.224744871 + -1
n = -1.224744871 + -1

Combine like terms: -1.224744871 + -1 = -2.224744871
n = -2.224744871

Simplifying
n = -2.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.224744871, -2.224744871}