8y^2-4y-3=0

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Solution for 8y^2-4y-3=0 equation:


Simplifying
8y2 + -4y + -3 = 0

Reorder the terms:
-3 + -4y + 8y2 = 0

Solving
-3 + -4y + 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'.
-0.375 + -0.5y + y2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.5y + 0.375 + y2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.5y + y2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.5y + y2 = 0 + 0.375
-0.5y + y2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-0.5y + y2 = 0.375

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = 0.375 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 0.375 + 0.0625

Combine like terms: 0.375 + 0.0625 = 0.4375
0.0625 + -0.5y + y2 = 0.4375

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(y + -0.25) equal to 0.661437828 and -0.661437828.

Subproblem 1

y + -0.25 = 0.661437828 Simplifying y + -0.25 = 0.661437828 Reorder the terms: -0.25 + y = 0.661437828 Solving -0.25 + y = 0.661437828 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = 0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = 0.661437828 + 0.25 y = 0.661437828 + 0.25 Combine like terms: 0.661437828 + 0.25 = 0.911437828 y = 0.911437828 Simplifying y = 0.911437828

Subproblem 2

y + -0.25 = -0.661437828 Simplifying y + -0.25 = -0.661437828 Reorder the terms: -0.25 + y = -0.661437828 Solving -0.25 + y = -0.661437828 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = -0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = -0.661437828 + 0.25 y = -0.661437828 + 0.25 Combine like terms: -0.661437828 + 0.25 = -0.411437828 y = -0.411437828 Simplifying y = -0.411437828

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.911437828, -0.411437828}

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