3n^2+3n-16877=0

Solution for 3n^2+3n-16877=0 equation:

Simplifying
3n2 + 3n + -16877 = 0

Reorder the terms:
-16877 + 3n + 3n2 = 0

Solving
-16877 + 3n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
-5625.666667 + n + n2 = 0

Move the constant term to the right:

Add '5625.666667' to each side of the equation.
-5625.666667 + n + 5625.666667 + n2 = 0 + 5625.666667

Reorder the terms:
-5625.666667 + 5625.666667 + n + n2 = 0 + 5625.666667

Combine like terms: -5625.666667 + 5625.666667 = 0.000000
0.000000 + n + n2 = 0 + 5625.666667
n + n2 = 0 + 5625.666667

Combine like terms: 0 + 5625.666667 = 5625.666667
n + n2 = 5625.666667

The n term is n.  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.
 + 0.25 + n2 = 5625.666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = 5625.666667 + 0.25

Combine like terms: 5625.666667 + 0.25 = 5625.916667
1.25 + n2 = 5625.916667

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 5625.916667

Calculate the square root of the right side: 75.006110864

Break this problem into two subproblems by setting 
(n + 0.5) equal to 75.006110864 and -75.006110864.

Subproblem 1
n + 0.5 = 75.006110864

Simplifying
n + 0.5 = 75.006110864

Reorder the terms:
0.5 + n = 75.006110864

Solving
0.5 + n = 75.006110864

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 = 75.006110864 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 75.006110864 + -0.5
n = 75.006110864 + -0.5

Combine like terms: 75.006110864 + -0.5 = 74.506110864
n = 74.506110864

Simplifying
n = 74.506110864

Subproblem 2
n + 0.5 = -75.006110864

Simplifying
n + 0.5 = -75.006110864

Reorder the terms:
0.5 + n = -75.006110864

Solving
0.5 + n = -75.006110864

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 = -75.006110864 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -75.006110864 + -0.5
n = -75.006110864 + -0.5

Combine like terms: -75.006110864 + -0.5 = -75.506110864
n = -75.506110864

Simplifying
n = -75.506110864

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {74.506110864, -75.506110864}