M1 is a spherical mass (43.8 kg) at the origin. M2 is also a spherical mass (15.4 kg) and is located on the x-axis at x = 57.0 m. At what value of x would a third mass with a 11.0 kg mass experience no net gravitational force due to M1 and M2?

here is what I did

G (m1 m3) / r1^2 = G (m2 m3) / r2^2
Sqrt (m1/m2) = r1/r2

r2 = 13.79 m
which is wrong :(
I do not know how to get it right.
Thanks for your support.
I really appreciate what you are doing.

In your last steps notice that r1 has conveniently disappeared. You have to keep it in your equation, What is the relationship between r1, r2 and r3? Think about it and you will see the way to the correct answer/

I'm not even getting your r2...

\sqrt{\frac{43.8}{15.4}} = \frac{r_1}{r_2}

Since M1 is at the origin, what you are looking for is the distance r1, the distance from M1, from the origin and also on the axis.

M2 is at 57 m away...

With this and the post of DrBob, you should be able to solve it. Post what you get! :)

I did not get it right. Well yeah I'm fool :)

No, you made a mistake and nobody is 'mistake-proof' ;)

Lol OK .