9y^2+11y-12=0

Solution for 9y^2+11y-12=0 equation:

Simplifying
9y2 + 11y + -12 = 0

Reorder the terms:
-12 + 11y + 9y2 = 0

Solving
-12 + 11y + 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'.
-1.333333333 + 1.222222222y + y2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 1.222222222y + 1.333333333 + y2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 1.222222222y + y2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 1.222222222y + y2 = 0 + 1.333333333
1.222222222y + y2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
1.222222222y + y2 = 1.333333333

The y term is 1.222222222y.  Take half its coefficient (0.611111111).
Square it (0.3734567900) and add it to both sides.

Add '0.3734567900' to each side of the equation.
1.222222222y + 0.3734567900 + y2 = 1.333333333 + 0.3734567900

Reorder the terms:
0.3734567900 + 1.222222222y + y2 = 1.333333333 + 0.3734567900

Combine like terms: 1.333333333 + 0.3734567900 = 1.706790123
0.3734567900 + 1.222222222y + y2 = 1.706790123

Factor a perfect square on the left side:
(y + 0.611111111)(y + 0.611111111) = 1.706790123

Calculate the square root of the right side: 1.306441779

Break this problem into two subproblems by setting 
(y + 0.611111111) equal to 1.306441779 and -1.306441779.

Subproblem 1
y + 0.611111111 = 1.306441779

Simplifying
y + 0.611111111 = 1.306441779

Reorder the terms:
0.611111111 + y = 1.306441779

Solving
0.611111111 + y = 1.306441779

Solving for variable 'y'.

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

Add '-0.611111111' to each side of the equation.
0.611111111 + -0.611111111 + y = 1.306441779 + -0.611111111

Combine like terms: 0.611111111 + -0.611111111 = 0.000000000
0.000000000 + y = 1.306441779 + -0.611111111
y = 1.306441779 + -0.611111111

Combine like terms: 1.306441779 + -0.611111111 = 0.695330668
y = 0.695330668

Simplifying
y = 0.695330668

Subproblem 2
y + 0.611111111 = -1.306441779

Simplifying
y + 0.611111111 = -1.306441779

Reorder the terms:
0.611111111 + y = -1.306441779

Solving
0.611111111 + y = -1.306441779

Solving for variable 'y'.

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

Add '-0.611111111' to each side of the equation.
0.611111111 + -0.611111111 + y = -1.306441779 + -0.611111111

Combine like terms: 0.611111111 + -0.611111111 = 0.000000000
0.000000000 + y = -1.306441779 + -0.611111111
y = -1.306441779 + -0.611111111

Combine like terms: -1.306441779 + -0.611111111 = -1.91755289
y = -1.91755289

Simplifying
y = -1.91755289

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.695330668, -1.91755289}