6n^2-3n-11=0

Solution for 6n^2-3n-11=0 equation:

Simplifying
6n2 + -3n + -11 = 0

Reorder the terms:
-11 + -3n + 6n2 = 0

Solving
-11 + -3n + 6n2 = 0

Solving for variable 'n'.

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

Divide each side by '6'.
-1.833333333 + -0.5n + n2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + -0.5n + 1.833333333 + n2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + -0.5n + n2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + -0.5n + n2 = 0 + 1.833333333
-0.5n + n2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
-0.5n + n2 = 1.833333333

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 = 1.833333333 + 0.0625

Reorder the terms:
0.0625 + -0.5n + n2 = 1.833333333 + 0.0625

Combine like terms: 1.833333333 + 0.0625 = 1.895833333
0.0625 + -0.5n + n2 = 1.895833333

Factor a perfect square on the left side:
(n + -0.25)(n + -0.25) = 1.895833333

Calculate the square root of the right side: 1.376892637

Break this problem into two subproblems by setting 
(n + -0.25) equal to 1.376892637 and -1.376892637.

Subproblem 1
n + -0.25 = 1.376892637

Simplifying
n + -0.25 = 1.376892637

Reorder the terms:
-0.25 + n = 1.376892637

Solving
-0.25 + n = 1.376892637

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 = 1.376892637 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = 1.376892637 + 0.25
n = 1.376892637 + 0.25

Combine like terms: 1.376892637 + 0.25 = 1.626892637
n = 1.626892637

Simplifying
n = 1.626892637

Subproblem 2
n + -0.25 = -1.376892637

Simplifying
n + -0.25 = -1.376892637

Reorder the terms:
-0.25 + n = -1.376892637

Solving
-0.25 + n = -1.376892637

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 = -1.376892637 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = -1.376892637 + 0.25
n = -1.376892637 + 0.25

Combine like terms: -1.376892637 + 0.25 = -1.126892637
n = -1.126892637

Simplifying
n = -1.126892637

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.626892637, -1.126892637}