15=w^2+3w-4

Solution for 15=w^2+3w-4 equation:

Simplifying
15 = w2 + 3w + -4

Reorder the terms:
15 = -4 + 3w + w2

Solving
15 = -4 + 3w + w2

Solving for variable 'w'.

Combine like terms: 15 + 4 = 19
19 + -3w + -1w2 = -4 + 3w + w2 + 4 + -3w + -1w2

Reorder the terms:
19 + -3w + -1w2 = -4 + 4 + 3w + -3w + w2 + -1w2

Combine like terms: -4 + 4 = 0
19 + -3w + -1w2 = 0 + 3w + -3w + w2 + -1w2
19 + -3w + -1w2 = 3w + -3w + w2 + -1w2

Combine like terms: 3w + -3w = 0
19 + -3w + -1w2 = 0 + w2 + -1w2
19 + -3w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
19 + -3w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-19 + 3w + w2 = 0

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 3w + 19 + w2 = 0 + 19

Reorder the terms:
-19 + 19 + 3w + w2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 3w + w2 = 0 + 19
3w + w2 = 0 + 19

Combine like terms: 0 + 19 = 19
3w + w2 = 19

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 19 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 19 + 2.25

Combine like terms: 19 + 2.25 = 21.25
2.25 + 3w + w2 = 21.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(w + 1.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
w + 1.5 = 4.609772229

Simplifying
w + 1.5 = 4.609772229

Reorder the terms:
1.5 + w = 4.609772229

Solving
1.5 + w = 4.609772229

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 4.609772229 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 4.609772229 + -1.5
w = 4.609772229 + -1.5

Combine like terms: 4.609772229 + -1.5 = 3.109772229
w = 3.109772229

Simplifying
w = 3.109772229

Subproblem 2
w + 1.5 = -4.609772229

Simplifying
w + 1.5 = -4.609772229

Reorder the terms:
1.5 + w = -4.609772229

Solving
1.5 + w = -4.609772229

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -4.609772229 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -4.609772229 + -1.5
w = -4.609772229 + -1.5

Combine like terms: -4.609772229 + -1.5 = -6.109772229
w = -6.109772229

Simplifying
w = -6.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.109772229, -6.109772229}