Manipulate

Your method is correct, but you can do it without dividing by K and then multiplying by K :

$F\,=\,K\cdot\frac{Q_1Q_2}{r^2} \\~\\ F\,=\,\frac{K(Q_1Q_2)}{r^2}$

                                  Multiply both sides of the equation by  r²

$Fr^2\,=\,K(Q_1Q_2)$

                                  Divide both sides of the equation by  F .

$r^2\,=\,\frac{K(Q_1Q_2)}{F}$

If we need to include both solutions for  r  ,  then we need to take the positive and negative square root of both sides.

$r\,=\,\pm\sqrt{\frac{K(Q_1Q_2)}{F}}$