Is it possible to find the point which is marked by question mark ? we know that the
s1(x)=s2(x) (the areas of the two triangles are equal)
I don't think so. The point common to both triangles can be moved to the left, increasing the area of the blue triangle and making the line from $(x_2,y_2)$ through the common point miss the point ? entirely. Then the point ? can move down to add the required area. In essence we have four unknowns-the coordinates of the common point and the coordinates of ? but only three constraints-the area equality and the fact that the two line segments through the common point are straight.