2w^2+8w-105=0

Solution for 2w^2+8w-105=0 equation:

Simplifying
2w2 + 8w + -105 = 0

Reorder the terms:
-105 + 8w + 2w2 = 0

Solving
-105 + 8w + 2w2 = 0

Solving for variable 'w'.

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

Divide each side by '2'.
-52.5 + 4w + w2 = 0

Move the constant term to the right:

Add '52.5' to each side of the equation.
-52.5 + 4w + 52.5 + w2 = 0 + 52.5

Reorder the terms:
-52.5 + 52.5 + 4w + w2 = 0 + 52.5

Combine like terms: -52.5 + 52.5 = 0.0
0.0 + 4w + w2 = 0 + 52.5
4w + w2 = 0 + 52.5

Combine like terms: 0 + 52.5 = 52.5
4w + w2 = 52.5

The w term is 4w.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4w + 4 + w2 = 52.5 + 4

Reorder the terms:
4 + 4w + w2 = 52.5 + 4

Combine like terms: 52.5 + 4 = 56.5
4 + 4w + w2 = 56.5

Factor a perfect square on the left side:
(w + 2)(w + 2) = 56.5

Calculate the square root of the right side: 7.516648189

Break this problem into two subproblems by setting 
(w + 2) equal to 7.516648189 and -7.516648189.

Subproblem 1
w + 2 = 7.516648189

Simplifying
w + 2 = 7.516648189

Reorder the terms:
2 + w = 7.516648189

Solving
2 + w = 7.516648189

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = 7.516648189 + -2

Combine like terms: 2 + -2 = 0
0 + w = 7.516648189 + -2
w = 7.516648189 + -2

Combine like terms: 7.516648189 + -2 = 5.516648189
w = 5.516648189

Simplifying
w = 5.516648189

Subproblem 2
w + 2 = -7.516648189

Simplifying
w + 2 = -7.516648189

Reorder the terms:
2 + w = -7.516648189

Solving
2 + w = -7.516648189

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = -7.516648189 + -2

Combine like terms: 2 + -2 = 0
0 + w = -7.516648189 + -2
w = -7.516648189 + -2

Combine like terms: -7.516648189 + -2 = -9.516648189
w = -9.516648189

Simplifying
w = -9.516648189

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.516648189, -9.516648189}