15y^2-20y-3=0

Solution for 15y^2-20y-3=0 equation:

Simplifying
15y2 + -20y + -3 = 0

Reorder the terms:
-3 + -20y + 15y2 = 0

Solving
-3 + -20y + 15y2 = 0

Solving for variable 'y'.

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

Divide each side by '15'.
-0.2 + -1.333333333y + y2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -1.333333333y + 0.2 + y2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -1.333333333y + y2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -1.333333333y + y2 = 0 + 0.2
-1.333333333y + y2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-1.333333333y + y2 = 0.2

The y term is -1.333333333y.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333y + 0.4444444442 + y2 = 0.2 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333y + y2 = 0.2 + 0.4444444442

Combine like terms: 0.2 + 0.4444444442 = 0.6444444442
0.4444444442 + -1.333333333y + y2 = 0.6444444442

Factor a perfect square on the left side:
(y + -0.6666666665)(y + -0.6666666665) = 0.6444444442

Calculate the square root of the right side: 0.802772972

Break this problem into two subproblems by setting 
(y + -0.6666666665) equal to 0.802772972 and -0.802772972.

Subproblem 1
y + -0.6666666665 = 0.802772972

Simplifying
y + -0.6666666665 = 0.802772972

Reorder the terms:
-0.6666666665 + y = 0.802772972

Solving
-0.6666666665 + y = 0.802772972

Solving for variable 'y'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + y = 0.802772972 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + y = 0.802772972 + 0.6666666665
y = 0.802772972 + 0.6666666665

Combine like terms: 0.802772972 + 0.6666666665 = 1.4694396385
y = 1.4694396385

Simplifying
y = 1.4694396385

Subproblem 2
y + -0.6666666665 = -0.802772972

Simplifying
y + -0.6666666665 = -0.802772972

Reorder the terms:
-0.6666666665 + y = -0.802772972

Solving
-0.6666666665 + y = -0.802772972

Solving for variable 'y'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + y = -0.802772972 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + y = -0.802772972 + 0.6666666665
y = -0.802772972 + 0.6666666665

Combine like terms: -0.802772972 + 0.6666666665 = -0.1361063055
y = -0.1361063055

Simplifying
y = -0.1361063055

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.4694396385, -0.1361063055}