3y^2-15y+4=0

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Solution for 3y^2-15y+4=0 equation: 


Simplifying
3y2 + -15y + 4 = 0

Reorder the terms:
4 + -15y + 3y2 = 0

Solving
4 + -15y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
1.333333333 + -5y + y2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -5y + -1.333333333 + y2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -5y + y2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -5y + y2 = 0 + -1.333333333
-5y + y2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-5y + y2 = -1.333333333

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = -1.333333333 + 6.25

Reorder the terms:
6.25 + -5y + y2 = -1.333333333 + 6.25

Combine like terms: -1.333333333 + 6.25 = 4.916666667
6.25 + -5y + y2 = 4.916666667

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 4.916666667

Calculate the square root of the right side: 2.217355783

Break this problem into two subproblems by setting 
(y + -2.5) equal to 2.217355783 and -2.217355783.


Subproblem 1
y + -2.5 = 2.217355783

Simplifying
y + -2.5 = 2.217355783

Reorder the terms:
-2.5 + y = 2.217355783

Solving
-2.5 + y = 2.217355783

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = 2.217355783 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 2.217355783 + 2.5
y = 2.217355783 + 2.5

Combine like terms: 2.217355783 + 2.5 = 4.717355783
y = 4.717355783

Simplifying
y = 4.717355783


Subproblem 2
y + -2.5 = -2.217355783

Simplifying
y + -2.5 = -2.217355783

Reorder the terms:
-2.5 + y = -2.217355783

Solving
-2.5 + y = -2.217355783

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = -2.217355783 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -2.217355783 + 2.5
y = -2.217355783 + 2.5

Combine like terms: -2.217355783 + 2.5 = 0.282644217
y = 0.282644217

Simplifying
y = 0.282644217


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.717355783, 0.282644217}

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