5y^2=9y+2

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

Simplifying
5y2 = 9y + 2

Reorder the terms:
5y2 = 2 + 9y

Solving
5y2 = 2 + 9y

Solving for variable 'y'.

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

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

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

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

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

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

Simplifying
-1 + -5y = 0

Solving
-1 + -5y = 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 + -5y = 0 + 1

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

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

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

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

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

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

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

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

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