0=20w^2+6w-112

Solution for 0=20w^2+6w-112 equation:

Simplifying
0 = 20w2 + 6w + -112

Reorder the terms:
0 = -112 + 6w + 20w2

Solving
0 = -112 + 6w + 20w2

Solving for variable 'w'.

Combine like terms: 0 + 112 = 112
112 + -6w + -20w2 = -112 + 6w + 20w2 + 112 + -6w + -20w2

Reorder the terms:
112 + -6w + -20w2 = -112 + 112 + 6w + -6w + 20w2 + -20w2

Combine like terms: -112 + 112 = 0
112 + -6w + -20w2 = 0 + 6w + -6w + 20w2 + -20w2
112 + -6w + -20w2 = 6w + -6w + 20w2 + -20w2

Combine like terms: 6w + -6w = 0
112 + -6w + -20w2 = 0 + 20w2 + -20w2
112 + -6w + -20w2 = 20w2 + -20w2

Combine like terms: 20w2 + -20w2 = 0
112 + -6w + -20w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(56 + -3w + -10w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(56 + -3w + -10w2)' equal to zero and attempt to solve:

Simplifying
56 + -3w + -10w2 = 0

Solving
56 + -3w + -10w2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-5.6 + 0.3w + w2 = 0.0

Move the constant term to the right:

Add '5.6' to each side of the equation.
-5.6 + 0.3w + 5.6 + w2 = 0.0 + 5.6

Reorder the terms:
-5.6 + 5.6 + 0.3w + w2 = 0.0 + 5.6

Combine like terms: -5.6 + 5.6 = 0.0
0.0 + 0.3w + w2 = 0.0 + 5.6
0.3w + w2 = 0.0 + 5.6

Combine like terms: 0.0 + 5.6 = 5.6
0.3w + w2 = 5.6

The w term is 0.3w.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3w + 0.0225 + w2 = 5.6 + 0.0225

Reorder the terms:
0.0225 + 0.3w + w2 = 5.6 + 0.0225

Combine like terms: 5.6 + 0.0225 = 5.6225
0.0225 + 0.3w + w2 = 5.6225

Factor a perfect square on the left side:
(w + 0.15)(w + 0.15) = 5.6225

Calculate the square root of the right side: 2.37118114

Break this problem into two subproblems by setting 
(w + 0.15) equal to 2.37118114 and -2.37118114.

Subproblem 1
w + 0.15 = 2.37118114

Simplifying
w + 0.15 = 2.37118114

Reorder the terms:
0.15 + w = 2.37118114

Solving
0.15 + w = 2.37118114

Solving for variable 'w'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + w = 2.37118114 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + w = 2.37118114 + -0.15
w = 2.37118114 + -0.15

Combine like terms: 2.37118114 + -0.15 = 2.22118114
w = 2.22118114

Simplifying
w = 2.22118114

Subproblem 2
w + 0.15 = -2.37118114

Simplifying
w + 0.15 = -2.37118114

Reorder the terms:
0.15 + w = -2.37118114

Solving
0.15 + w = -2.37118114

Solving for variable 'w'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + w = -2.37118114 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + w = -2.37118114 + -0.15
w = -2.37118114 + -0.15

Combine like terms: -2.37118114 + -0.15 = -2.52118114
w = -2.52118114

Simplifying
w = -2.52118114

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.22118114, -2.52118114}
Solution
w = {2.22118114, -2.52118114}