2y^2=9y+5

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

Simplifying
2y2 = 9y + 5

Reorder the terms:
2y2 = 5 + 9y

Solving
2y2 = 5 + 9y

Solving for variable 'y'.

Reorder the terms:
-5 + -9y + 2y2 = 5 + 9y + -5 + -9y

Reorder the terms:
-5 + -9y + 2y2 = 5 + -5 + 9y + -9y

Combine like terms: 5 + -5 = 0
-5 + -9y + 2y2 = 0 + 9y + -9y
-5 + -9y + 2y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
-5 + -9y + 2y2 = 0

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

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

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 0

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

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

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

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

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

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

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

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

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

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

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

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