9w^2+10w-8=0

Solution for 9w^2+10w-8=0 equation:

Simplifying
9w2 + 10w + -8 = 0

Reorder the terms:
-8 + 10w + 9w2 = 0

Solving
-8 + 10w + 9w2 = 0

Solving for variable 'w'.

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

Divide each side by '9'.
-0.8888888889 + 1.111111111w + w2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + 1.111111111w + 0.8888888889 + w2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + 1.111111111w + w2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + 1.111111111w + w2 = 0 + 0.8888888889
1.111111111w + w2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
1.111111111w + w2 = 0.8888888889

The w term is 1.111111111w.  Take half its coefficient (0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
1.111111111w + 0.3086419752 + w2 = 0.8888888889 + 0.3086419752

Reorder the terms:
0.3086419752 + 1.111111111w + w2 = 0.8888888889 + 0.3086419752

Combine like terms: 0.8888888889 + 0.3086419752 = 1.1975308641
0.3086419752 + 1.111111111w + w2 = 1.1975308641

Factor a perfect square on the left side:
(w + 0.5555555555)(w + 0.5555555555) = 1.1975308641

Calculate the square root of the right side: 1.094317533

Break this problem into two subproblems by setting 
(w + 0.5555555555) equal to 1.094317533 and -1.094317533.

Subproblem 1
w + 0.5555555555 = 1.094317533

Simplifying
w + 0.5555555555 = 1.094317533

Reorder the terms:
0.5555555555 + w = 1.094317533

Solving
0.5555555555 + w = 1.094317533

Solving for variable 'w'.

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

Add '-0.5555555555' to each side of the equation.
0.5555555555 + -0.5555555555 + w = 1.094317533 + -0.5555555555

Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000
0.0000000000 + w = 1.094317533 + -0.5555555555
w = 1.094317533 + -0.5555555555

Combine like terms: 1.094317533 + -0.5555555555 = 0.5387619775
w = 0.5387619775

Simplifying
w = 0.5387619775

Subproblem 2
w + 0.5555555555 = -1.094317533

Simplifying
w + 0.5555555555 = -1.094317533

Reorder the terms:
0.5555555555 + w = -1.094317533

Solving
0.5555555555 + w = -1.094317533

Solving for variable 'w'.

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

Add '-0.5555555555' to each side of the equation.
0.5555555555 + -0.5555555555 + w = -1.094317533 + -0.5555555555

Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000
0.0000000000 + w = -1.094317533 + -0.5555555555
w = -1.094317533 + -0.5555555555

Combine like terms: -1.094317533 + -0.5555555555 = -1.6498730885
w = -1.6498730885

Simplifying
w = -1.6498730885

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.5387619775, -1.6498730885}