Elementry Electrostatics question
Careful! I think you are picking the wrong root. You want solve k*(q1q3)/a^2=k*(q2q3)/(10-a)^2 if a<0 is the coordinate of the point. If you solve that you get 4.14 and -24.14. Since you assumed a<0 the one to pick is -24.14. If you call a the distance of the point from the origin then you solve k*(q1q3)/a^2=k*(q2q3)/(10+a)^2 and assuming a>0. You get -4.14, 24.14 and pick the positive one.