Intersection between 2 circles

I am writting a C++ program in Visual Basics 6.0 that solves the intersection of two circles.

I have this formula

(x-a2)^2+(y-b2)^2-Radius2^2=(x-a1)^2+(y-b1)^2-Radius1^2=0.

If I do my arithmatics correctly then

X = ( -a^2 - b^2 + R1^2 - R2^2 - 2y(-b2+b1) ) / 2(-a2 + a1)

The problem is that I don't know Y so how could I solve for X?

or do I take equation X and plug it into the original equation and solve for Y?

But if I solve for Y then I have 2 answers and then do I plug it back in to the original equation and get X?

or there is another way to do this?

Help is appreciated

Thanks.