Determining velocity of frame in spacetime

[b2386]

I have a short question regarding a spacetime interval in relativity.

I am told that event 1 is 2 meters of time and 1 meter of distance from the origin. Event 2 is 5 meters of time and 6 meters of distance from the origin. The question asks me to find the velocity of an observer that sees these events at the same time since they are spacelike (as opposed to timelike).

I began by using the equation $$\Delta{t^2}-\Delta{x^2}=\Delta{t^2}-\Delta{x^2}$$ Using the measurements from the rest frame gives me $$3^2-5^2=\Delta{t^2}-\Delta{x^2}$$

I know that t should be 0 in the new frame, giving me d = 4. So my question is, how can I use this information to determine the velocity of this new frame?

 

[b2386]

Well, I just found the answer using the equation for the stretch factor but is there a more direct way of obtaining the correct answer of v=.6?

EDIT: One more thing. When using the stretch factor equation of $$\gamma=\frac{1}{(1-v^2)^{1/2}}$$, how do I know whether gamma is 4/5 or 5/4 by looking at the length contraction in this problem?

Thanks