I am not clear about exactly what you are trying to do.
It sounds like you have three (x,y) coordinates. From those three points, you would like to determine the quadratic equation that produced those points:
y = a*x^2 + b*x + c
Once you have the equation, you would then like to find the roots of this equation.
Have I understood your question correctly?
If so, the problem is not really one of interpolation; it is more one of root-finding. In fact, roots of a quadratic equation are easy to find; equations for doing so are usually covered in high-school.
In your situation, the most difficult part is going to be determining the equation. For that, you would simply solve three equations in three unknowns for the coefficients: a, b, and c. Once you've got those, the rest is simple.