Solve for x in terms of the other symbols:

Question

rsx^2 + s^2 x + rtx + st = 0

Answer 1

rsx^2 + (rt+s^2)x + st = 0

Now just use the quadratic formula:

x = [-(rt+s^2)±√((rt+s^2)^2 - 4rs^2t)]/2rs

= [-(rt+s^2)±(rt-s^2))]/2rs

= (-rt-s^2+rt-s^2)/2rs = -s/r
or
= (-rt-s^2-rt+s^2)/2rs = -t/s