Find the maximum number of students the class can contain. A pair of students is selected at random from a class.The probability that the pair selected will consist of one male and one female student is $\frac{10}{19}$.Find the maximum number of students the class can contain.

Let the class has $x$ boy students and $y$ girl students.
Probability of selecting a boy student and a girl student is $\frac{x}{x+y}\times\frac{y}{x+y}=\frac{xy}{(x+y)}$
When a pair of students is selected at random from a class,there are four possibilities $BB,GG,GB,BG$.so one boy and one girl has probability $\frac{1}{4}$
So $\frac{1}{4}\times\frac{xy}{(x+y)}=\frac{10}{19}$

I am stuck here and i dont know how to find the maximum number of students in the class.I am not even sure if my steps are correct.

Let $x$ and $y$ be the number of boys and girls.We find max $x+y$.we have $\dfrac{2xy}{(x+y)(x+y-1)}=\dfrac{10}{19} \Rightarrow \dfrac{5}{19} \leq \dfrac{m^2}{4m(m-1)}$.Can you solve this inequality? Here we have $m=x+y$.
