Hi,
i am working in a zero crossing estimation in my project and i got a problem in that and it has to be implemented in hardware.

The problem is,

we have 3 points (x1,y1), (x2,y2), (x3,y3) with a transistion between the second and third point from positive to negative then we have to interpolate where is the zero crossing (ie., (x,0) , the x coordinate when y=0).
here all the values are in binary format and so we cannot implement neither multiplications nor divisions in solving for the interpolated values using interpolation methods. but we can use 1 or 2 multiplications but divisions are strictly not allowed.
i have solved using lagranges interpolation formula, where i have eleminated the division by taking LCM. but i got strucked up with solving quadratic equation.

it should take at the maximum of 3 steps better if got less than that.
i tried it solving using Newton Raphsons method but i got strucked up with the division involved in it, is there any way of solving it without the division part in it.

is there any other method which does not involve division and solves the quadratic equation.

kindly give some solution or suggestions.

thanking you,
sreenivas