3y^2-9y+4=0

Solution for 3y^2-9y+4=0 equation:

Simplifying
3y2 + -9y + 4 = 0

Reorder the terms:
4 + -9y + 3y2 = 0

Solving
4 + -9y + 3y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
1.333333333 + -3y + y2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -3y + -1.333333333 + y2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -3y + y2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -3y + y2 = 0 + -1.333333333
-3y + y2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-3y + y2 = -1.333333333

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -1.333333333 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -1.333333333 + 2.25

Combine like terms: -1.333333333 + 2.25 = 0.916666667
2.25 + -3y + y2 = 0.916666667

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 0.916666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(y + -1.5) equal to 0.957427108 and -0.957427108.

Subproblem 1
y + -1.5 = 0.957427108

Simplifying
y + -1.5 = 0.957427108

Reorder the terms:
-1.5 + y = 0.957427108

Solving
-1.5 + y = 0.957427108

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 0.957427108 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 0.957427108 + 1.5
y = 0.957427108 + 1.5

Combine like terms: 0.957427108 + 1.5 = 2.457427108
y = 2.457427108

Simplifying
y = 2.457427108

Subproblem 2
y + -1.5 = -0.957427108

Simplifying
y + -1.5 = -0.957427108

Reorder the terms:
-1.5 + y = -0.957427108

Solving
-1.5 + y = -0.957427108

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -0.957427108 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -0.957427108 + 1.5
y = -0.957427108 + 1.5

Combine like terms: -0.957427108 + 1.5 = 0.542572892
y = 0.542572892

Simplifying
y = 0.542572892

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.457427108, 0.542572892}