We are given to solve for :
The first step is to multiply through by :
Now, subtract through by :
Factor the left side:
Can you proceed from here?
I am trying to simplify this to express a as a function of t,r,p. It is killing me. Any help would be most appreciated.
a^2=[(at)^2 + r^2]/p
Edit: This problem is trivial, but I am also looking for a solution given the additional constraint,
t=ab,
I am confused, because your solution gives a=zero when b=0, but if we simply let b=0 and solve from the initial equation, we get a simple solution that is only zero when r=0, i.e.
a=SQRT(r^2/p)
Edit: I see that the quadratic formula does not apply when b=0.