Here we go, Find sin2a, cos2a, and tan2a given tan(theta)= -24/7. OK, I know sin2a=2sin a cos a and tan x=sin x/cos x, and tan also =y/x. Knowing that the first thing I did was r=sqrt of -24^2+7^2 which =625. 625 is going to be my denominators for sin2a and cos2a. If possible can someone show me a step by step way of doing this so I may apply those steps with the rest of my homework??

You've found r, so now you can determine sin(theta) and cos(theta). Now just plug these values into the formulas. You know sin 2a = 2*sin a*cos a. Also, cos 2a = cos^2 a - sin^2 a. Lastly, tan 2a = (sin 2a)/(cos 2a).