0=3y^2-9y+31

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Solution for 0=3y^2-9y+31 equation: 


Simplifying
0 = 3y2 + -9y + 31

Reorder the terms:
0 = 31 + -9y + 3y2

Solving
0 = 31 + -9y + 3y2

Solving for variable 'y'.

Combine like terms: 0 + -31 = -31
-31 + 9y + -3y2 = 31 + -9y + 3y2 + -31 + 9y + -3y2

Reorder the terms:
-31 + 9y + -3y2 = 31 + -31 + -9y + 9y + 3y2 + -3y2

Combine like terms: 31 + -31 = 0
-31 + 9y + -3y2 = 0 + -9y + 9y + 3y2 + -3y2
-31 + 9y + -3y2 = -9y + 9y + 3y2 + -3y2

Combine like terms: -9y + 9y = 0
-31 + 9y + -3y2 = 0 + 3y2 + -3y2
-31 + 9y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-31 + 9y + -3y2 = 0

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

Divide each side by '-3'.
10.33333333 + -3y + y2 = 0

Move the constant term to the right:

Add '-10.33333333' to each side of the equation.
10.33333333 + -3y + -10.33333333 + y2 = 0 + -10.33333333

Reorder the terms:
10.33333333 + -10.33333333 + -3y + y2 = 0 + -10.33333333

Combine like terms: 10.33333333 + -10.33333333 = 0.00000000
0.00000000 + -3y + y2 = 0 + -10.33333333
-3y + y2 = 0 + -10.33333333

Combine like terms: 0 + -10.33333333 = -10.33333333
-3y + y2 = -10.33333333

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -10.33333333 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -10.33333333 + 2.25

Combine like terms: -10.33333333 + 2.25 = -8.08333333
2.25 + -3y + y2 = -8.08333333

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = -8.08333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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