9y^2+6y-4=0

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Solution for 9y^2+6y-4=0 equation: 


Simplifying
9y2 + 6y + -4 = 0

Reorder the terms:
-4 + 6y + 9y2 = 0

Solving
-4 + 6y + 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'.
-0.4444444444 + 0.6666666667y + y2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + 0.6666666667y + 0.4444444444 + y2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + 0.6666666667y + y2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + 0.6666666667y + y2 = 0 + 0.4444444444
0.6666666667y + y2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
0.6666666667y + y2 = 0.4444444444

The y term is 0.6666666667y.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667y + 0.1111111112 + y2 = 0.4444444444 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667y + y2 = 0.4444444444 + 0.1111111112

Combine like terms: 0.4444444444 + 0.1111111112 = 0.5555555556
0.1111111112 + 0.6666666667y + y2 = 0.5555555556

Factor a perfect square on the left side:
(y + 0.3333333334)(y + 0.3333333334) = 0.5555555556

Calculate the square root of the right side: 0.745355993

Break this problem into two subproblems by setting 
(y + 0.3333333334) equal to 0.745355993 and -0.745355993.


Subproblem 1
y + 0.3333333334 = 0.745355993

Simplifying
y + 0.3333333334 = 0.745355993

Reorder the terms:
0.3333333334 + y = 0.745355993

Solving
0.3333333334 + y = 0.745355993

Solving for variable 'y'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + y = 0.745355993 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + y = 0.745355993 + -0.3333333334
y = 0.745355993 + -0.3333333334

Combine like terms: 0.745355993 + -0.3333333334 = 0.4120226596
y = 0.4120226596

Simplifying
y = 0.4120226596


Subproblem 2
y + 0.3333333334 = -0.745355993

Simplifying
y + 0.3333333334 = -0.745355993

Reorder the terms:
0.3333333334 + y = -0.745355993

Solving
0.3333333334 + y = -0.745355993

Solving for variable 'y'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + y = -0.745355993 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + y = -0.745355993 + -0.3333333334
y = -0.745355993 + -0.3333333334

Combine like terms: -0.745355993 + -0.3333333334 = -1.0786893264
y = -1.0786893264

Simplifying
y = -1.0786893264


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.4120226596, -1.0786893264}

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