8y^2-7y-4=0

Solution for 8y^2-7y-4=0 equation:

Simplifying
8y2 + -7y + -4 = 0

Reorder the terms:
-4 + -7y + 8y2 = 0

Solving
-4 + -7y + 8y2 = 0

Solving for variable 'y'.

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

Divide each side by '8'.
-0.5 + -0.875y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.875y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.875y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.875y + y2 = 0 + 0.5
-0.875y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.875y + y2 = 0.5

The y term is -0.875y.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875y + 0.19140625 + y2 = 0.5 + 0.19140625

Reorder the terms:
0.19140625 + -0.875y + y2 = 0.5 + 0.19140625

Combine like terms: 0.5 + 0.19140625 = 0.69140625
0.19140625 + -0.875y + y2 = 0.69140625

Factor a perfect square on the left side:
(y + -0.4375)(y + -0.4375) = 0.69140625

Calculate the square root of the right side: 0.831508418

Break this problem into two subproblems by setting 
(y + -0.4375) equal to 0.831508418 and -0.831508418.

Subproblem 1
y + -0.4375 = 0.831508418

Simplifying
y + -0.4375 = 0.831508418

Reorder the terms:
-0.4375 + y = 0.831508418

Solving
-0.4375 + y = 0.831508418

Solving for variable 'y'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + y = 0.831508418 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + y = 0.831508418 + 0.4375
y = 0.831508418 + 0.4375

Combine like terms: 0.831508418 + 0.4375 = 1.269008418
y = 1.269008418

Simplifying
y = 1.269008418

Subproblem 2
y + -0.4375 = -0.831508418

Simplifying
y + -0.4375 = -0.831508418

Reorder the terms:
-0.4375 + y = -0.831508418

Solving
-0.4375 + y = -0.831508418

Solving for variable 'y'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + y = -0.831508418 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + y = -0.831508418 + 0.4375
y = -0.831508418 + 0.4375

Combine like terms: -0.831508418 + 0.4375 = -0.394008418
y = -0.394008418

Simplifying
y = -0.394008418

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.269008418, -0.394008418}