5n^2+6n-24=0

Solution for 5n^2+6n-24=0 equation:

Simplifying
5n2 + 6n + -24 = 0

Reorder the terms:
-24 + 6n + 5n2 = 0

Solving
-24 + 6n + 5n2 = 0

Solving for variable 'n'.

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

Divide each side by '5'.
-4.8 + 1.2n + n2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + 1.2n + 4.8 + n2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + 1.2n + n2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + 1.2n + n2 = 0 + 4.8
1.2n + n2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
1.2n + n2 = 4.8

The n term is 1.2n.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2n + 0.36 + n2 = 4.8 + 0.36

Reorder the terms:
0.36 + 1.2n + n2 = 4.8 + 0.36

Combine like terms: 4.8 + 0.36 = 5.16
0.36 + 1.2n + n2 = 5.16

Factor a perfect square on the left side:
(n + 0.6)(n + 0.6) = 5.16

Calculate the square root of the right side: 2.271563338

Break this problem into two subproblems by setting 
(n + 0.6) equal to 2.271563338 and -2.271563338.

Subproblem 1
n + 0.6 = 2.271563338

Simplifying
n + 0.6 = 2.271563338

Reorder the terms:
0.6 + n = 2.271563338

Solving
0.6 + n = 2.271563338

Solving for variable 'n'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + n = 2.271563338 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + n = 2.271563338 + -0.6
n = 2.271563338 + -0.6

Combine like terms: 2.271563338 + -0.6 = 1.671563338
n = 1.671563338

Simplifying
n = 1.671563338

Subproblem 2
n + 0.6 = -2.271563338

Simplifying
n + 0.6 = -2.271563338

Reorder the terms:
0.6 + n = -2.271563338

Solving
0.6 + n = -2.271563338

Solving for variable 'n'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + n = -2.271563338 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + n = -2.271563338 + -0.6
n = -2.271563338 + -0.6

Combine like terms: -2.271563338 + -0.6 = -2.871563338
n = -2.871563338

Simplifying
n = -2.871563338

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.671563338, -2.871563338}