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x2 + 4x + y2 - 6y = 3

You need to be more clear about your question:

Are you trying to find the properties of the curve it defines?

x2 + 4x + y2 - 6y = 3

∴ x2 + 4x + 4 + y2 - 6y + 9 = 16

∴ (x + 2)2 + (y - 3)2 = 42

∴ This describes a circle with a radius of 4, and a center point of (-2, 3)

Did you want to solve for y?

(x + 2)2 + (y - 3)2 = 42

∴ (y - 3)2 = 16 - (x + 2)2

∴ y - 3 = ± [16 - (x + 2)2]1/2

∴ y = 3 ± [16 - (x + 2)2]1/2

Did you want to solve for x?

(x + 2)2 + (y - 3)2 = 42

∴ (x + 2)2 = 16 - (y - 3)2

∴ x + 2 = ± [16 - (y - 3)2]1/2

∴ x = -2 ± [16 - (y - 3)2]1/2

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