3y^2-28y+3=0

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Solution for 3y^2-28y+3=0 equation: 


Simplifying
3y2 + -28y + 3 = 0

Reorder the terms:
3 + -28y + 3y2 = 0

Solving
3 + -28y + 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 + -9.333333333y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -9.333333333y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -9.333333333y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9.333333333y + y2 = 0 + -1
-9.333333333y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-9.333333333y + y2 = -1

The y term is -9.333333333y.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333y + 21.77777778 + y2 = -1 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333y + y2 = -1 + 21.77777778

Combine like terms: -1 + 21.77777778 = 20.77777778
21.77777778 + -9.333333333y + y2 = 20.77777778

Factor a perfect square on the left side:
(y + -4.666666667)(y + -4.666666667) = 20.77777778

Calculate the square root of the right side: 4.558264777

Break this problem into two subproblems by setting 
(y + -4.666666667) equal to 4.558264777 and -4.558264777.


Subproblem 1
y + -4.666666667 = 4.558264777

Simplifying
y + -4.666666667 = 4.558264777

Reorder the terms:
-4.666666667 + y = 4.558264777

Solving
-4.666666667 + y = 4.558264777

Solving for variable 'y'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + y = 4.558264777 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + y = 4.558264777 + 4.666666667
y = 4.558264777 + 4.666666667

Combine like terms: 4.558264777 + 4.666666667 = 9.224931444
y = 9.224931444

Simplifying
y = 9.224931444


Subproblem 2
y + -4.666666667 = -4.558264777

Simplifying
y + -4.666666667 = -4.558264777

Reorder the terms:
-4.666666667 + y = -4.558264777

Solving
-4.666666667 + y = -4.558264777

Solving for variable 'y'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + y = -4.558264777 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + y = -4.558264777 + 4.666666667
y = -4.558264777 + 4.666666667

Combine like terms: -4.558264777 + 4.666666667 = 0.10840189
y = 0.10840189

Simplifying
y = 0.10840189


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.224931444, 0.10840189}

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