I think what Mo's getting at though is what's the algorithm.

If all the equations to be solved are quadratics as per the example, it's dead simple.

The equation is y= ax^2 + bx + c and then

x1= (-b + (b^2 - 4ac)^.5) / 2a

x2= (-b - (b^2 - 4ac)^.5) / 2a

Simple code will do that arithmetic.

First you should have the code do 2 things...

1) check for a=0 since the equation is then a straight line not a parabola and it's illegal to divide by the 2a if a=0

2) check if the square root term b^2 - 4ac is <0, because if it is there is no real square root and the curve does not cut the x axis.