2y^2-8y-3=0

Solution for 2y^2-8y-3=0 equation:

Simplifying
2y2 + -8y + -3 = 0

Reorder the terms:
-3 + -8y + 2y2 = 0

Solving
-3 + -8y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-1.5 + -4y + y2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -4y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -4y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -4y + y2 = 0 + 1.5
-4y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-4y + y2 = 1.5

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 = 1.5 + 4

Reorder the terms:
4 + -4y + y2 = 1.5 + 4

Combine like terms: 1.5 + 4 = 5.5
4 + -4y + y2 = 5.5

Factor a perfect square on the left side:
(y + -2)(y + -2) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(y + -2) equal to 2.34520788 and -2.34520788.

Subproblem 1
y + -2 = 2.34520788

Simplifying
y + -2 = 2.34520788

Reorder the terms:
-2 + y = 2.34520788

Solving
-2 + y = 2.34520788

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 = 2.34520788 + 2

Combine like terms: -2 + 2 = 0
0 + y = 2.34520788 + 2
y = 2.34520788 + 2

Combine like terms: 2.34520788 + 2 = 4.34520788
y = 4.34520788

Simplifying
y = 4.34520788

Subproblem 2
y + -2 = -2.34520788

Simplifying
y + -2 = -2.34520788

Reorder the terms:
-2 + y = -2.34520788

Solving
-2 + y = -2.34520788

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 = -2.34520788 + 2

Combine like terms: -2 + 2 = 0
0 + y = -2.34520788 + 2
y = -2.34520788 + 2

Combine like terms: -2.34520788 + 2 = -0.34520788
y = -0.34520788

Simplifying
y = -0.34520788

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.34520788, -0.34520788}