How Do You Calculate Velocity in Lorentz Transformations?

[Nuclear#1]

I'm studying for my modern physics final and this problem is giving me trouble;

Q: In a frame S, two events have spatial separation deltaX= 600m, delta y and delta z = 0, and a temporal separation deltaT= 1micro second. A second frame S' is moving along the same axis with nonzero speed v (0'x' is parallel to 0x). In S' it is found that the spatial separation is deltaX' is also 600m. What are v and deltaT'?

My attempts have been using x'=gamma(x-vt), now I plug in the known data and try to manipulate the equation into a quadratic I can solve, but every time I do it I wind up not getting anywhere close to being correct. What does the proper quadratic formula look like? The correct answers are v = 0.8C and T = -1 micro second. I just need help finding how to find the velocity. Please help, any thing would be helpful.

 

[George Jones]

Can you first find $\Delta T'$ by using invariance of the spacetime interval?

 

[Nuclear#1]

Sorry but I figured it out, I was making algebraic errors. The quadratic turns into; 1.25v^2 - cv = 0. with v = 0 and v = 2.4E8, which is 0.8c. I didn't think you could find delta T' first, so I went about it doing it this way because it was the recommended method. Sorry for the inconvenience.

 

[George Jones]

Great!

Actually, it is trivial to find delta T' first, which then eliminates the need to use terms quadratic in v.