Y=5Y^2+108

Solution for Y=5Y^2+108 equation:

Simplifying
Y = 5Y2 + 108

Reorder the terms:
Y = 108 + 5Y2

Solving
Y = 108 + 5Y2

Solving for variable 'Y'.

Reorder the terms:
-108 + Y + -5Y2 = 108 + 5Y2 + -108 + -5Y2

Reorder the terms:
-108 + Y + -5Y2 = 108 + -108 + 5Y2 + -5Y2

Combine like terms: 108 + -108 = 0
-108 + Y + -5Y2 = 0 + 5Y2 + -5Y2
-108 + Y + -5Y2 = 5Y2 + -5Y2

Combine like terms: 5Y2 + -5Y2 = 0
-108 + Y + -5Y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
21.6 + -0.2Y + Y2 = 0

Move the constant term to the right:

Add '-21.6' to each side of the equation.
21.6 + -0.2Y + -21.6 + Y2 = 0 + -21.6

Reorder the terms:
21.6 + -21.6 + -0.2Y + Y2 = 0 + -21.6

Combine like terms: 21.6 + -21.6 = 0.0
0.0 + -0.2Y + Y2 = 0 + -21.6
-0.2Y + Y2 = 0 + -21.6

Combine like terms: 0 + -21.6 = -21.6
-0.2Y + Y2 = -21.6

The Y term is Y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.2Y + 0.25 + Y2 = -21.6 + 0.25

Reorder the terms:
0.25 + -0.2Y + Y2 = -21.6 + 0.25

Combine like terms: -21.6 + 0.25 = -21.35
0.25 + -0.2Y + Y2 = -21.35

Factor a perfect square on the left side:
(Y + 0.5)(Y + 0.5) = -21.35

Can't calculate square root of the right side.

The solution to this equation could not be determined.