2w^2+4w-21-w^2-7w-140=0

Solution for 2w^2+4w-21-w^2-7w-140=0 equation:

Simplifying
2w2 + 4w + -21 + -1w2 + -7w + -140 = 0

Reorder the terms:
-21 + -140 + 4w + -7w + 2w2 + -1w2 = 0

Combine like terms: -21 + -140 = -161
-161 + 4w + -7w + 2w2 + -1w2 = 0

Combine like terms: 4w + -7w = -3w
-161 + -3w + 2w2 + -1w2 = 0

Combine like terms: 2w2 + -1w2 = 1w2
-161 + -3w + 1w2 = 0

Solving
-161 + -3w + 1w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '161' to each side of the equation.
-161 + -3w + 161 + w2 = 0 + 161

Reorder the terms:
-161 + 161 + -3w + w2 = 0 + 161

Combine like terms: -161 + 161 = 0
0 + -3w + w2 = 0 + 161
-3w + w2 = 0 + 161

Combine like terms: 0 + 161 = 161
-3w + w2 = 161

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 = 161 + 2.25

Reorder the terms:
2.25 + -3w + w2 = 161 + 2.25

Combine like terms: 161 + 2.25 = 163.25
2.25 + -3w + w2 = 163.25

Factor a perfect square on the left side:
(w + -1.5)(w + -1.5) = 163.25

Calculate the square root of the right side: 12.776932339

Break this problem into two subproblems by setting 
(w + -1.5) equal to 12.776932339 and -12.776932339.

Subproblem 1
w + -1.5 = 12.776932339

Simplifying
w + -1.5 = 12.776932339

Reorder the terms:
-1.5 + w = 12.776932339

Solving
-1.5 + w = 12.776932339

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 = 12.776932339 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = 12.776932339 + 1.5
w = 12.776932339 + 1.5

Combine like terms: 12.776932339 + 1.5 = 14.276932339
w = 14.276932339

Simplifying
w = 14.276932339

Subproblem 2
w + -1.5 = -12.776932339

Simplifying
w + -1.5 = -12.776932339

Reorder the terms:
-1.5 + w = -12.776932339

Solving
-1.5 + w = -12.776932339

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 = -12.776932339 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = -12.776932339 + 1.5
w = -12.776932339 + 1.5

Combine like terms: -12.776932339 + 1.5 = -11.276932339
w = -11.276932339

Simplifying
w = -11.276932339

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {14.276932339, -11.276932339}