5w^2=9w+2

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

Simplifying
5w2 = 9w + 2

Reorder the terms:
5w2 = 2 + 9w

Solving
5w2 = 2 + 9w

Solving for variable 'w'.

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

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

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

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

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

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

Simplifying
-1 + -5w = 0

Solving
-1 + -5w = 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 + -5w = 0 + 1

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

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

Divide each side by '-5'.
w = -0.2

Simplifying
w = -0.2
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-0.2, 2}