The given equation is
[tex]w=\frac{va}{r^2+a^2}[/tex]We need to solve it for a
let us cross multiply the two sides
[tex]w(r^2+a^2)=va[/tex]Divide both sides by w
[tex]r^2+a^2=\frac{va}{w}[/tex]Subtract r^2 from both sides
[tex]a^2=\frac{va}{w}-r^2[/tex]