9y^2-27y+2=0

Solution for 9y^2-27y+2=0 equation:

Simplifying
9y2 + -27y + 2 = 0

Reorder the terms:
2 + -27y + 9y2 = 0

Solving
2 + -27y + 9y2 = 0

Solving for variable 'y'.

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

Divide each side by '9'.
0.2222222222 + -3y + y2 = 0

Move the constant term to the right:

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -3y + -0.2222222222 + y2 = 0 + -0.2222222222

Reorder the terms:
0.2222222222 + -0.2222222222 + -3y + y2 = 0 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + -3y + y2 = 0 + -0.2222222222
-3y + y2 = 0 + -0.2222222222

Combine like terms: 0 + -0.2222222222 = -0.2222222222
-3y + y2 = -0.2222222222

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 = -0.2222222222 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -0.2222222222 + 2.25

Combine like terms: -0.2222222222 + 2.25 = 2.0277777778
2.25 + -3y + y2 = 2.0277777778

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 2.0277777778

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.424000624 and -1.424000624.

Subproblem 1
y + -1.5 = 1.424000624

Simplifying
y + -1.5 = 1.424000624

Reorder the terms:
-1.5 + y = 1.424000624

Solving
-1.5 + y = 1.424000624

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 = 1.424000624 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.424000624 + 1.5
y = 1.424000624 + 1.5

Combine like terms: 1.424000624 + 1.5 = 2.924000624
y = 2.924000624

Simplifying
y = 2.924000624

Subproblem 2
y + -1.5 = -1.424000624

Simplifying
y + -1.5 = -1.424000624

Reorder the terms:
-1.5 + y = -1.424000624

Solving
-1.5 + y = -1.424000624

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 = -1.424000624 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.424000624 + 1.5
y = -1.424000624 + 1.5

Combine like terms: -1.424000624 + 1.5 = 0.075999376
y = 0.075999376

Simplifying
y = 0.075999376

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.924000624, 0.075999376}