9y^2+14y-6=0

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Solution for 9y^2+14y-6=0 equation:


Simplifying
9y2 + 14y + -6 = 0

Reorder the terms:
-6 + 14y + 9y2 = 0

Solving
-6 + 14y + 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'.
-0.6666666667 + 1.555555556y + y2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 1.555555556y + 0.6666666667 + y2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 1.555555556y + y2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 1.555555556y + y2 = 0 + 0.6666666667
1.555555556y + y2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
1.555555556y + y2 = 0.6666666667

The y term is 1.555555556y.  Take half its coefficient (0.777777778).
Square it (0.6049382720) and add it to both sides.

Add '0.6049382720' to each side of the equation.
1.555555556y + 0.6049382720 + y2 = 0.6666666667 + 0.6049382720

Reorder the terms:
0.6049382720 + 1.555555556y + y2 = 0.6666666667 + 0.6049382720

Combine like terms: 0.6666666667 + 0.6049382720 = 1.2716049387
0.6049382720 + 1.555555556y + y2 = 1.2716049387

Factor a perfect square on the left side:
(y + 0.777777778)(y + 0.777777778) = 1.2716049387

Calculate the square root of the right side: 1.127654619

Break this problem into two subproblems by setting 
(y + 0.777777778) equal to 1.127654619 and -1.127654619.

Subproblem 1

y + 0.777777778 = 1.127654619 Simplifying y + 0.777777778 = 1.127654619 Reorder the terms: 0.777777778 + y = 1.127654619 Solving 0.777777778 + y = 1.127654619 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + y = 1.127654619 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + y = 1.127654619 + -0.777777778 y = 1.127654619 + -0.777777778 Combine like terms: 1.127654619 + -0.777777778 = 0.349876841 y = 0.349876841 Simplifying y = 0.349876841

Subproblem 2

y + 0.777777778 = -1.127654619 Simplifying y + 0.777777778 = -1.127654619 Reorder the terms: 0.777777778 + y = -1.127654619 Solving 0.777777778 + y = -1.127654619 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + y = -1.127654619 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + y = -1.127654619 + -0.777777778 y = -1.127654619 + -0.777777778 Combine like terms: -1.127654619 + -0.777777778 = -1.905432397 y = -1.905432397 Simplifying y = -1.905432397

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.349876841, -1.905432397}

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