jmc

Multiplying both sides by 2 and by 5 to eliminate the fractions gives $$5(r-45)=2(3-2r).$$ Expanding both sides gives $5r-225=6-4r$. Adding $4r$ and 225 to both sides gives $9r=231$, so $r=\frac{231}{9}=\boxed{\frac{77}{3}}$.