4n^2+n-15=0

Solution for 4n^2+n-15=0 equation:

Simplifying
4n2 + n + -15 = 0

Reorder the terms:
-15 + n + 4n2 = 0

Solving
-15 + n + 4n2 = 0

Solving for variable 'n'.

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

Divide each side by '4'.
-3.75 + 0.25n + n2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 0.25n + 3.75 + n2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 0.25n + n2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 0.25n + n2 = 0 + 3.75
0.25n + n2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
0.25n + n2 = 3.75

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.
0.25n + 0.25 + n2 = 3.75 + 0.25

Reorder the terms:
0.25 + 0.25n + n2 = 3.75 + 0.25

Combine like terms: 3.75 + 0.25 = 4
0.25 + 0.25n + n2 = 4

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(n + 0.5) equal to 2 and -2.

Subproblem 1
n + 0.5 = 2

Simplifying
n + 0.5 = 2

Reorder the terms:
0.5 + n = 2

Solving
0.5 + n = 2

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 = 2 + -0.5

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

Combine like terms: 2 + -0.5 = 1.5
n = 1.5

Simplifying
n = 1.5

Subproblem 2
n + 0.5 = -2

Simplifying
n + 0.5 = -2

Reorder the terms:
0.5 + n = -2

Solving
0.5 + n = -2

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 = -2 + -0.5

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

Combine like terms: -2 + -0.5 = -2.5
n = -2.5

Simplifying
n = -2.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.5, -2.5}