Swans

Let total number of swans be $x$ .

Swans playing on shore of tank= $\frac{7}{2}\sqrt{x}$

Swans fighting= $2$

$x=2+\frac{7}{2}\sqrt{x}$

$7\sqrt{x}=2x-4$

Squaring both sides, $49x=4x^{2}-16x+16$ $4x^{2}-65x+16=0$

On solving this quadratic equation, we get $x=16,\frac{1}{4}$ . Since number of swans cannot be in fraction, $x=\boxed{\boxed{16}}$

Note that we got an extra solution $x=\frac{1}{4}$ because of squaring which usually ends up with some wrong solutions.