y^2-2y-90=0

Solution for y^2-2y-90=0 equation:

Simplifying
y2 + -2y + -90 = 0

Reorder the terms:
-90 + -2y + y2 = 0

Solving
-90 + -2y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -2y + 90 + y2 = 0 + 90

Reorder the terms:
-90 + 90 + -2y + y2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -2y + y2 = 0 + 90
-2y + y2 = 0 + 90

Combine like terms: 0 + 90 = 90
-2y + y2 = 90

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 90 + 1

Reorder the terms:
1 + -2y + y2 = 90 + 1

Combine like terms: 90 + 1 = 91
1 + -2y + y2 = 91

Factor a perfect square on the left side:
(y + -1)(y + -1) = 91

Calculate the square root of the right side: 9.539392014

Break this problem into two subproblems by setting 
(y + -1) equal to 9.539392014 and -9.539392014.

Subproblem 1
y + -1 = 9.539392014

Simplifying
y + -1 = 9.539392014

Reorder the terms:
-1 + y = 9.539392014

Solving
-1 + y = 9.539392014

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 9.539392014 + 1

Combine like terms: -1 + 1 = 0
0 + y = 9.539392014 + 1
y = 9.539392014 + 1

Combine like terms: 9.539392014 + 1 = 10.539392014
y = 10.539392014

Simplifying
y = 10.539392014

Subproblem 2
y + -1 = -9.539392014

Simplifying
y + -1 = -9.539392014

Reorder the terms:
-1 + y = -9.539392014

Solving
-1 + y = -9.539392014

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -9.539392014 + 1

Combine like terms: -1 + 1 = 0
0 + y = -9.539392014 + 1
y = -9.539392014 + 1

Combine like terms: -9.539392014 + 1 = -8.539392014
y = -8.539392014

Simplifying
y = -8.539392014

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.539392014, -8.539392014}