Solve w= (va)/(r^2+a^2) for a.
I applied the quadratic formula
a= (v/w +- sqrt (v^2/w^2 - 4*(-wr^2)) /2
and I have the answer as a= (v+/- sqrt[v^2+4w^2r^2]/w
a^2 -(v/w)a - r^2 =0
I think your "b^2 = 4ac" term is wrong.
It should be
sqrt [(v/w)^2 + 4r^2]