2.4y^2-12.72y+3.6=0

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Solution for 2.4y^2-12.72y+3.6=0 equation: 


Simplifying
2.4y2 + -12.72y + 3.6 = 0

Reorder the terms:
3.6 + -12.72y + 2.4y2 = 0

Solving
3.6 + -12.72y + 2.4y2 = 0

Solving for variable 'y'.

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

Divide each side by '2.4'.
1.5 + -5.3y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -5.3y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -5.3y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -5.3y + y2 = 0 + -1.5
-5.3y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-5.3y + y2 = -1.5

The y term is -5.3y.  Take half its coefficient (-2.65).
Square it (7.0225) and add it to both sides.

Add '7.0225' to each side of the equation.
-5.3y + 7.0225 + y2 = -1.5 + 7.0225

Reorder the terms:
7.0225 + -5.3y + y2 = -1.5 + 7.0225

Combine like terms: -1.5 + 7.0225 = 5.5225
7.0225 + -5.3y + y2 = 5.5225

Factor a perfect square on the left side:
(y + -2.65)(y + -2.65) = 5.5225

Calculate the square root of the right side: 2.35

Break this problem into two subproblems by setting 
(y + -2.65) equal to 2.35 and -2.35.


Subproblem 1
y + -2.65 = 2.35

Simplifying
y + -2.65 = 2.35

Reorder the terms:
-2.65 + y = 2.35

Solving
-2.65 + y = 2.35

Solving for variable 'y'.

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

Add '2.65' to each side of the equation.
-2.65 + 2.65 + y = 2.35 + 2.65

Combine like terms: -2.65 + 2.65 = 0.00
0.00 + y = 2.35 + 2.65
y = 2.35 + 2.65

Combine like terms: 2.35 + 2.65 = 5
y = 5

Simplifying
y = 5


Subproblem 2
y + -2.65 = -2.35

Simplifying
y + -2.65 = -2.35

Reorder the terms:
-2.65 + y = -2.35

Solving
-2.65 + y = -2.35

Solving for variable 'y'.

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

Add '2.65' to each side of the equation.
-2.65 + 2.65 + y = -2.35 + 2.65

Combine like terms: -2.65 + 2.65 = 0.00
0.00 + y = -2.35 + 2.65
y = -2.35 + 2.65

Combine like terms: -2.35 + 2.65 = 0.3
y = 0.3

Simplifying
y = 0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5, 0.3}

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