y^2-2y-6=0

Solution for y^2-2y-6=0 equation:

Simplifying
y2 + -2y + -6 = 0

Reorder the terms:
-6 + -2y + y2 = 0

Solving
-6 + -2y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + -2y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2y + y2 = 0 + 6
-2y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2y + y2 = 6

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 = 6 + 1

Reorder the terms:
1 + -2y + y2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2y + y2 = 7

Factor a perfect square on the left side:
(y + -1)(y + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
y + -1 = 2.645751311

Simplifying
y + -1 = 2.645751311

Reorder the terms:
-1 + y = 2.645751311

Solving
-1 + y = 2.645751311

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 = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + y = 2.645751311 + 1
y = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
y = 3.645751311

Simplifying
y = 3.645751311

Subproblem 2
y + -1 = -2.645751311

Simplifying
y + -1 = -2.645751311

Reorder the terms:
-1 + y = -2.645751311

Solving
-1 + y = -2.645751311

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 = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + y = -2.645751311 + 1
y = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
y = -1.645751311

Simplifying
y = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.645751311, -1.645751311}