8w^2+34w-9=0

Solution for 8w^2+34w-9=0 equation:

Simplifying
8w2 + 34w + -9 = 0

Reorder the terms:
-9 + 34w + 8w2 = 0

Solving
-9 + 34w + 8w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + -2w)(1 + -4w) = 0

Subproblem 1
Set the factor '(-9 + -2w)' equal to zero and attempt to solve:

Simplifying
-9 + -2w = 0

Solving
-9 + -2w = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2w = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2w = 0 + 9
-2w = 0 + 9

Combine like terms: 0 + 9 = 9
-2w = 9

Divide each side by '-2'.
w = -4.5

Simplifying
w = -4.5
Subproblem 2
Set the factor '(1 + -4w)' equal to zero and attempt to solve:

Simplifying
1 + -4w = 0

Solving
1 + -4w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4w = 0 + -1
-4w = 0 + -1

Combine like terms: 0 + -1 = -1
-4w = -1

Divide each side by '-4'.
w = 0.25

Simplifying
w = 0.25
Solution
w = {-4.5, 0.25}