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Equation of a circle
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Why would two solutions mean it didn't work?  It's a circle.
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It would be unusual to get one solution
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Your method is correct. Draw the picture of the circle and see how many points there are where x = 0.
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I have vague memories of being confused by this when I was a high-school student, and then the confusion gave way to a kind of wonder as I realized that the multiple roots were exactly right for describing the situation.

Similarly, when you are solving a quadratic to find out when a projectile will hit the ground, you will get two solutions, because the solutions tell you when the projectile is *at* ground level -- and it must have been launched sometime!
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Consider the fact that the line x=0 intersects your circle at two points.
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For a circle, every x, except for 2 values, yields 2 values of y.

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