Blue socks needed for an even chance of a red pair

A drawer contains $3$ red socks and $n$ blue socks. Two socks are taken at random without replacement, and the chance that both are red is $\tfrac12$. What is $n$?

$n=1$. The chance of two reds is $\tfrac{3}{n+3}\cdot\tfrac{2}{n+2}$. Setting this to $\tfrac12$ gives $(n+2)(n+3)=12$, i.e. $n^2+5n-6=0$, whose only non-negative root is $1$.