5y^2=9y-4

Solution for 5y^2=9y-4 equation:

Simplifying
5y2 = 9y + -4

Reorder the terms:
5y2 = -4 + 9y

Solving
5y2 = -4 + 9y

Solving for variable 'y'.

Reorder the terms:
4 + -9y + 5y2 = -4 + 9y + 4 + -9y

Reorder the terms:
4 + -9y + 5y2 = -4 + 4 + 9y + -9y

Combine like terms: -4 + 4 = 0
4 + -9y + 5y2 = 0 + 9y + -9y
4 + -9y + 5y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
4 + -9y + 5y2 = 0

Factor a trinomial.
(4 + -5y)(1 + -1y) = 0

Subproblem 1
Set the factor '(4 + -5y)' equal to zero and attempt to solve:

Simplifying
4 + -5y = 0

Solving
4 + -5y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5y = 0 + -4
-5y = 0 + -4

Combine like terms: 0 + -4 = -4
-5y = -4

Divide each side by '-5'.
y = 0.8

Simplifying
y = 0.8
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {0.8, 1}