15y^2-24y-20=0

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Solution for 15y^2-24y-20=0 equation: 


Simplifying
15y2 + -24y + -20 = 0

Reorder the terms:
-20 + -24y + 15y2 = 0

Solving
-20 + -24y + 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'.
-1.333333333 + -1.6y + y2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -1.6y + 1.333333333 + y2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -1.6y + y2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -1.6y + y2 = 0 + 1.333333333
-1.6y + y2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-1.6y + y2 = 1.333333333

The y term is -1.6y.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6y + 0.64 + y2 = 1.333333333 + 0.64

Reorder the terms:
0.64 + -1.6y + y2 = 1.333333333 + 0.64

Combine like terms: 1.333333333 + 0.64 = 1.973333333
0.64 + -1.6y + y2 = 1.973333333

Factor a perfect square on the left side:
(y + -0.8)(y + -0.8) = 1.973333333

Calculate the square root of the right side: 1.404753834

Break this problem into two subproblems by setting 
(y + -0.8) equal to 1.404753834 and -1.404753834.


Subproblem 1
y + -0.8 = 1.404753834

Simplifying
y + -0.8 = 1.404753834

Reorder the terms:
-0.8 + y = 1.404753834

Solving
-0.8 + y = 1.404753834

Solving for variable 'y'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + y = 1.404753834 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + y = 1.404753834 + 0.8
y = 1.404753834 + 0.8

Combine like terms: 1.404753834 + 0.8 = 2.204753834
y = 2.204753834

Simplifying
y = 2.204753834


Subproblem 2
y + -0.8 = -1.404753834

Simplifying
y + -0.8 = -1.404753834

Reorder the terms:
-0.8 + y = -1.404753834

Solving
-0.8 + y = -1.404753834

Solving for variable 'y'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + y = -1.404753834 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + y = -1.404753834 + 0.8
y = -1.404753834 + 0.8

Combine like terms: -1.404753834 + 0.8 = -0.604753834
y = -0.604753834

Simplifying
y = -0.604753834


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.204753834, -0.604753834}

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