5y^2-10y-12=0

Solution for 5y^2-10y-12=0 equation:

Simplifying
5y2 + -10y + -12 = 0

Reorder the terms:
-12 + -10y + 5y2 = 0

Solving
-12 + -10y + 5y2 = 0

Solving for variable 'y'.

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

Divide each side by '5'.
-2.4 + -2y + y2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + -2y + 2.4 + y2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + -2y + y2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + -2y + y2 = 0 + 2.4
-2y + y2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
-2y + y2 = 2.4

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 = 2.4 + 1

Reorder the terms:
1 + -2y + y2 = 2.4 + 1

Combine like terms: 2.4 + 1 = 3.4
1 + -2y + y2 = 3.4

Factor a perfect square on the left side:
(y + -1)(y + -1) = 3.4

Calculate the square root of the right side: 1.843908891

Break this problem into two subproblems by setting 
(y + -1) equal to 1.843908891 and -1.843908891.

Subproblem 1
y + -1 = 1.843908891

Simplifying
y + -1 = 1.843908891

Reorder the terms:
-1 + y = 1.843908891

Solving
-1 + y = 1.843908891

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 = 1.843908891 + 1

Combine like terms: -1 + 1 = 0
0 + y = 1.843908891 + 1
y = 1.843908891 + 1

Combine like terms: 1.843908891 + 1 = 2.843908891
y = 2.843908891

Simplifying
y = 2.843908891

Subproblem 2
y + -1 = -1.843908891

Simplifying
y + -1 = -1.843908891

Reorder the terms:
-1 + y = -1.843908891

Solving
-1 + y = -1.843908891

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 = -1.843908891 + 1

Combine like terms: -1 + 1 = 0
0 + y = -1.843908891 + 1
y = -1.843908891 + 1

Combine like terms: -1.843908891 + 1 = -0.843908891
y = -0.843908891

Simplifying
y = -0.843908891

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.843908891, -0.843908891}