12y^2-37y+18=0

Solution for 12y^2-37y+18=0 equation:

Simplifying
12y2 + -37y + 18 = 0

Reorder the terms:
18 + -37y + 12y2 = 0

Solving
18 + -37y + 12y2 = 0

Solving for variable 'y'.

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

Divide each side by '12'.
1.5 + -3.083333333y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -3.083333333y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -3.083333333y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -3.083333333y + y2 = 0 + -1.5
-3.083333333y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-3.083333333y + y2 = -1.5

The y term is -3.083333333y.  Take half its coefficient (-1.541666667).
Square it (2.376736112) and add it to both sides.

Add '2.376736112' to each side of the equation.
-3.083333333y + 2.376736112 + y2 = -1.5 + 2.376736112

Reorder the terms:
2.376736112 + -3.083333333y + y2 = -1.5 + 2.376736112

Combine like terms: -1.5 + 2.376736112 = 0.876736112
2.376736112 + -3.083333333y + y2 = 0.876736112

Factor a perfect square on the left side:
(y + -1.541666667)(y + -1.541666667) = 0.876736112

Calculate the square root of the right side: 0.936341878

Break this problem into two subproblems by setting 
(y + -1.541666667) equal to 0.936341878 and -0.936341878.

Subproblem 1
y + -1.541666667 = 0.936341878

Simplifying
y + -1.541666667 = 0.936341878

Reorder the terms:
-1.541666667 + y = 0.936341878

Solving
-1.541666667 + y = 0.936341878

Solving for variable 'y'.

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

Add '1.541666667' to each side of the equation.
-1.541666667 + 1.541666667 + y = 0.936341878 + 1.541666667

Combine like terms: -1.541666667 + 1.541666667 = 0.000000000
0.000000000 + y = 0.936341878 + 1.541666667
y = 0.936341878 + 1.541666667

Combine like terms: 0.936341878 + 1.541666667 = 2.478008545
y = 2.478008545

Simplifying
y = 2.478008545

Subproblem 2
y + -1.541666667 = -0.936341878

Simplifying
y + -1.541666667 = -0.936341878

Reorder the terms:
-1.541666667 + y = -0.936341878

Solving
-1.541666667 + y = -0.936341878

Solving for variable 'y'.

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

Add '1.541666667' to each side of the equation.
-1.541666667 + 1.541666667 + y = -0.936341878 + 1.541666667

Combine like terms: -1.541666667 + 1.541666667 = 0.000000000
0.000000000 + y = -0.936341878 + 1.541666667
y = -0.936341878 + 1.541666667

Combine like terms: -0.936341878 + 1.541666667 = 0.605324789
y = 0.605324789

Simplifying
y = 0.605324789

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.478008545, 0.605324789}