2w^2=9w+5

Solution for 2w^2=9w+5 equation:

Simplifying
2w2 = 9w + 5

Reorder the terms:
2w2 = 5 + 9w

Solving
2w2 = 5 + 9w

Solving for variable 'w'.

Reorder the terms:
-5 + -9w + 2w2 = 5 + 9w + -5 + -9w

Reorder the terms:
-5 + -9w + 2w2 = 5 + -5 + 9w + -9w

Combine like terms: 5 + -5 = 0
-5 + -9w + 2w2 = 0 + 9w + -9w
-5 + -9w + 2w2 = 9w + -9w

Combine like terms: 9w + -9w = 0
-5 + -9w + 2w2 = 0

Factor a trinomial.
(-1 + -2w)(5 + -1w) = 0

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

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 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 + -2w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2w = 0 + 1
-2w = 0 + 1

Combine like terms: 0 + 1 = 1
-2w = 1

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-0.5, 5}