9w^2=4w+5

Solution for 9w^2=4w+5 equation:

Simplifying
9w2 = 4w + 5

Reorder the terms:
9w2 = 5 + 4w

Solving
9w2 = 5 + 4w

Solving for variable 'w'.

Reorder the terms:
-5 + -4w + 9w2 = 5 + 4w + -5 + -4w

Reorder the terms:
-5 + -4w + 9w2 = 5 + -5 + 4w + -4w

Combine like terms: 5 + -5 = 0
-5 + -4w + 9w2 = 0 + 4w + -4w
-5 + -4w + 9w2 = 4w + -4w

Combine like terms: 4w + -4w = 0
-5 + -4w + 9w2 = 0

Factor a trinomial.
(-5 + -9w)(1 + -1w) = 0

Subproblem 1
Set the factor '(-5 + -9w)' equal to zero and attempt to solve:

Simplifying
-5 + -9w = 0

Solving
-5 + -9w = 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 + -9w = 0 + 5

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

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

Divide each side by '-9'.
w = -0.5555555556

Simplifying
w = -0.5555555556
Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

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

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

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

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

Simplifying
w = 1
Solution
w = {-0.5555555556, 1}