3y^2=5(y-2)

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Solution for 3y^2=5(y-2) equation: 


Simplifying
3y2 = 5(y + -2)

Reorder the terms:
3y2 = 5(-2 + y)
3y2 = (-2 * 5 + y * 5)
3y2 = (-10 + 5y)

Solving
3y2 = -10 + 5y

Solving for variable 'y'.

Reorder the terms:
10 + -5y + 3y2 = -10 + 5y + 10 + -5y

Reorder the terms:
10 + -5y + 3y2 = -10 + 10 + 5y + -5y

Combine like terms: -10 + 10 = 0
10 + -5y + 3y2 = 0 + 5y + -5y
10 + -5y + 3y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
10 + -5y + 3y2 = 0

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

Divide each side by '3'.
3.333333333 + -1.666666667y + y2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -1.666666667y + -3.333333333 + y2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -1.666666667y + y2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -1.666666667y + y2 = 0 + -3.333333333
-1.666666667y + y2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-1.666666667y + y2 = -3.333333333

The y term is -1.666666667y.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667y + 0.6944444447 + y2 = -3.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667y + y2 = -3.333333333 + 0.6944444447

Combine like terms: -3.333333333 + 0.6944444447 = -2.6388888883
0.6944444447 + -1.666666667y + y2 = -2.6388888883

Factor a perfect square on the left side:
(y + -0.8333333335)(y + -0.8333333335) = -2.6388888883

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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