y^2-4y-6=0

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

Simplifying
y2 + -4y + -6 = 0

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

Solving
-6 + -4y + 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 + -4y + 6 + y2 = 0 + 6

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

Combine like terms: -6 + 6 = 0
0 + -4y + y2 = 0 + 6
-4y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
-4y + y2 = 6

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 6 + 4

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

Combine like terms: 6 + 4 = 10
4 + -4y + y2 = 10

Factor a perfect square on the left side:
(y + -2)(y + -2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(y + -2) equal to 3.16227766 and -3.16227766.

Subproblem 1
y + -2 = 3.16227766

Simplifying
y + -2 = 3.16227766

Reorder the terms:
-2 + y = 3.16227766

Solving
-2 + y = 3.16227766

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 3.16227766 + 2

Combine like terms: -2 + 2 = 0
0 + y = 3.16227766 + 2
y = 3.16227766 + 2

Combine like terms: 3.16227766 + 2 = 5.16227766
y = 5.16227766

Simplifying
y = 5.16227766

Subproblem 2
y + -2 = -3.16227766

Simplifying
y + -2 = -3.16227766

Reorder the terms:
-2 + y = -3.16227766

Solving
-2 + y = -3.16227766

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -3.16227766 + 2

Combine like terms: -2 + 2 = 0
0 + y = -3.16227766 + 2
y = -3.16227766 + 2

Combine like terms: -3.16227766 + 2 = -1.16227766
y = -1.16227766

Simplifying
y = -1.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.16227766, -1.16227766}