9y^2-15+5=y+9

Solution for 9y^2-15+5=y+9 equation:

Simplifying
9y2 + -15 + 5 = y + 9

Reorder the terms:
-15 + 5 + 9y2 = y + 9

Combine like terms: -15 + 5 = -10
-10 + 9y2 = y + 9

Reorder the terms:
-10 + 9y2 = 9 + y

Solving
-10 + 9y2 = 9 + y

Solving for variable 'y'.

Reorder the terms:
-10 + -9 + -1y + 9y2 = 9 + y + -9 + -1y

Combine like terms: -10 + -9 = -19
-19 + -1y + 9y2 = 9 + y + -9 + -1y

Reorder the terms:
-19 + -1y + 9y2 = 9 + -9 + y + -1y

Combine like terms: 9 + -9 = 0
-19 + -1y + 9y2 = 0 + y + -1y
-19 + -1y + 9y2 = y + -1y

Combine like terms: y + -1y = 0
-19 + -1y + 9y2 = 0

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

Divide each side by '9'.
-2.111111111 + -0.1111111111y + y2 = 0

Move the constant term to the right:

Add '2.111111111' to each side of the equation.
-2.111111111 + -0.1111111111y + 2.111111111 + y2 = 0 + 2.111111111

Reorder the terms:
-2.111111111 + 2.111111111 + -0.1111111111y + y2 = 0 + 2.111111111

Combine like terms: -2.111111111 + 2.111111111 = 0.000000000
0.000000000 + -0.1111111111y + y2 = 0 + 2.111111111
-0.1111111111y + y2 = 0 + 2.111111111

Combine like terms: 0 + 2.111111111 = 2.111111111
-0.1111111111y + y2 = 2.111111111

The y term is -0.1111111111y.  Take half its coefficient (-0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
-0.1111111111y + 0.003086419752 + y2 = 2.111111111 + 0.003086419752

Reorder the terms:
0.003086419752 + -0.1111111111y + y2 = 2.111111111 + 0.003086419752

Combine like terms: 2.111111111 + 0.003086419752 = 2.114197530752
0.003086419752 + -0.1111111111y + y2 = 2.114197530752

Factor a perfect square on the left side:
(y + -0.05555555555)(y + -0.05555555555) = 2.114197530752

Calculate the square root of the right side: 1.454028036

Break this problem into two subproblems by setting 
(y + -0.05555555555) equal to 1.454028036 and -1.454028036.

Subproblem 1
y + -0.05555555555 = 1.454028036

Simplifying
y + -0.05555555555 = 1.454028036

Reorder the terms:
-0.05555555555 + y = 1.454028036

Solving
-0.05555555555 + y = 1.454028036

Solving for variable 'y'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + y = 1.454028036 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + y = 1.454028036 + 0.05555555555
y = 1.454028036 + 0.05555555555

Combine like terms: 1.454028036 + 0.05555555555 = 1.50958359155
y = 1.50958359155

Simplifying
y = 1.50958359155

Subproblem 2
y + -0.05555555555 = -1.454028036

Simplifying
y + -0.05555555555 = -1.454028036

Reorder the terms:
-0.05555555555 + y = -1.454028036

Solving
-0.05555555555 + y = -1.454028036

Solving for variable 'y'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + y = -1.454028036 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + y = -1.454028036 + 0.05555555555
y = -1.454028036 + 0.05555555555

Combine like terms: -1.454028036 + 0.05555555555 = -1.39847248045
y = -1.39847248045

Simplifying
y = -1.39847248045

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.50958359155, -1.39847248045}