8y^2-6y-10=0

Solution for 8y^2-6y-10=0 equation:

Simplifying
8y2 + -6y + -10 = 0

Reorder the terms:
-10 + -6y + 8y2 = 0

Solving
-10 + -6y + 8y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -3y + 4y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -3y + 4y2)' equal to zero and attempt to solve:

Simplifying
-5 + -3y + 4y2 = 0

Solving
-5 + -3y + 4y2 = 0

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

Divide each side by '4'.
-1.25 + -0.75y + y2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -0.75y + 1.25 + y2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -0.75y + y2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -0.75y + y2 = 0 + 1.25
-0.75y + y2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-0.75y + y2 = 1.25

The y term is -0.75y.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75y + 0.140625 + y2 = 1.25 + 0.140625

Reorder the terms:
0.140625 + -0.75y + y2 = 1.25 + 0.140625

Combine like terms: 1.25 + 0.140625 = 1.390625
0.140625 + -0.75y + y2 = 1.390625

Factor a perfect square on the left side:
(y + -0.375)(y + -0.375) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(y + -0.375) equal to 1.179247642 and -1.179247642.

Subproblem 1
y + -0.375 = 1.179247642

Simplifying
y + -0.375 = 1.179247642

Reorder the terms:
-0.375 + y = 1.179247642

Solving
-0.375 + y = 1.179247642

Solving for variable 'y'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + y = 1.179247642 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + y = 1.179247642 + 0.375
y = 1.179247642 + 0.375

Combine like terms: 1.179247642 + 0.375 = 1.554247642
y = 1.554247642

Simplifying
y = 1.554247642

Subproblem 2
y + -0.375 = -1.179247642

Simplifying
y + -0.375 = -1.179247642

Reorder the terms:
-0.375 + y = -1.179247642

Solving
-0.375 + y = -1.179247642

Solving for variable 'y'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + y = -1.179247642 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + y = -1.179247642 + 0.375
y = -1.179247642 + 0.375

Combine like terms: -1.179247642 + 0.375 = -0.804247642
y = -0.804247642

Simplifying
y = -0.804247642

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.554247642, -0.804247642}
Solution
y = {1.554247642, -0.804247642}