8y^2-12y-9=0

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Solution for 8y^2-12y-9=0 equation: 


Simplifying
8y2 + -12y + -9 = 0

Reorder the terms:
-9 + -12y + 8y2 = 0

Solving
-9 + -12y + 8y2 = 0

Solving for variable 'y'.

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

Divide each side by '8'.
-1.125 + -1.5y + y2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -1.5y + 1.125 + y2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -1.5y + y2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -1.5y + y2 = 0 + 1.125
-1.5y + y2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-1.5y + y2 = 1.125

The y term is -1.5y.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = 1.125 + 0.5625

Reorder the terms:
0.5625 + -1.5y + y2 = 1.125 + 0.5625

Combine like terms: 1.125 + 0.5625 = 1.6875
0.5625 + -1.5y + y2 = 1.6875

Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = 1.6875

Calculate the square root of the right side: 1.299038106

Break this problem into two subproblems by setting 
(y + -0.75) equal to 1.299038106 and -1.299038106.


Subproblem 1
y + -0.75 = 1.299038106

Simplifying
y + -0.75 = 1.299038106

Reorder the terms:
-0.75 + y = 1.299038106

Solving
-0.75 + y = 1.299038106

Solving for variable 'y'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = 1.299038106 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = 1.299038106 + 0.75
y = 1.299038106 + 0.75

Combine like terms: 1.299038106 + 0.75 = 2.049038106
y = 2.049038106

Simplifying
y = 2.049038106


Subproblem 2
y + -0.75 = -1.299038106

Simplifying
y + -0.75 = -1.299038106

Reorder the terms:
-0.75 + y = -1.299038106

Solving
-0.75 + y = -1.299038106

Solving for variable 'y'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = -1.299038106 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = -1.299038106 + 0.75
y = -1.299038106 + 0.75

Combine like terms: -1.299038106 + 0.75 = -0.549038106
y = -0.549038106

Simplifying
y = -0.549038106


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.049038106, -0.549038106}

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