9n^2+7n-56=0

Solution for 9n^2+7n-56=0 equation:

Simplifying
9n2 + 7n + -56 = 0

Reorder the terms:
-56 + 7n + 9n2 = 0

Solving
-56 + 7n + 9n2 = 0

Solving for variable 'n'.

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

Divide each side by '9'.
-6.222222222 + 0.7777777778n + n2 = 0

Move the constant term to the right:

Add '6.222222222' to each side of the equation.
-6.222222222 + 0.7777777778n + 6.222222222 + n2 = 0 + 6.222222222

Reorder the terms:
-6.222222222 + 6.222222222 + 0.7777777778n + n2 = 0 + 6.222222222

Combine like terms: -6.222222222 + 6.222222222 = 0.000000000
0.000000000 + 0.7777777778n + n2 = 0 + 6.222222222
0.7777777778n + n2 = 0 + 6.222222222

Combine like terms: 0 + 6.222222222 = 6.222222222
0.7777777778n + n2 = 6.222222222

The n term is 0.7777777778n.  Take half its coefficient (0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
0.7777777778n + 0.1512345679 + n2 = 6.222222222 + 0.1512345679

Reorder the terms:
0.1512345679 + 0.7777777778n + n2 = 6.222222222 + 0.1512345679

Combine like terms: 6.222222222 + 0.1512345679 = 6.3734567899
0.1512345679 + 0.7777777778n + n2 = 6.3734567899

Factor a perfect square on the left side:
(n + 0.3888888889)(n + 0.3888888889) = 6.3734567899

Calculate the square root of the right side: 2.524570615

Break this problem into two subproblems by setting 
(n + 0.3888888889) equal to 2.524570615 and -2.524570615.

Subproblem 1
n + 0.3888888889 = 2.524570615

Simplifying
n + 0.3888888889 = 2.524570615

Reorder the terms:
0.3888888889 + n = 2.524570615

Solving
0.3888888889 + n = 2.524570615

Solving for variable 'n'.

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

Add '-0.3888888889' to each side of the equation.
0.3888888889 + -0.3888888889 + n = 2.524570615 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + n = 2.524570615 + -0.3888888889
n = 2.524570615 + -0.3888888889

Combine like terms: 2.524570615 + -0.3888888889 = 2.1356817261
n = 2.1356817261

Simplifying
n = 2.1356817261

Subproblem 2
n + 0.3888888889 = -2.524570615

Simplifying
n + 0.3888888889 = -2.524570615

Reorder the terms:
0.3888888889 + n = -2.524570615

Solving
0.3888888889 + n = -2.524570615

Solving for variable 'n'.

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

Add '-0.3888888889' to each side of the equation.
0.3888888889 + -0.3888888889 + n = -2.524570615 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + n = -2.524570615 + -0.3888888889
n = -2.524570615 + -0.3888888889

Combine like terms: -2.524570615 + -0.3888888889 = -2.9134595039
n = -2.9134595039

Simplifying
n = -2.9134595039

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.1356817261, -2.9134595039}