Find the roots of the following quadratic equations by the factorisation method:
$\frac{2}{5} x^{2}-x-\frac{3}{5}=0$

$A$ train,travelling at a uniform speed for $360\, km$,would have taken $48\, min$ less to travel the same distance,if its speed were $5\, km/h$ more. Find the original speed of the train (in $km/h$).

$A$ two-digit number is such that the product of its digits is $6$. When $9$ is subtracted from the number,the resulting number is the number obtained by interchanging the digits. Find the original number.

The sum of two natural numbers is $5$ and the sum of their reciprocals is $\frac{5}{6}$. Find those numbers.

If both the roots of $25x^{2} - x(m - 2) - 1 = 0$ are opposite,then $m = \ldots$

The lengths of the sides forming the right angle of a right-angled triangle are $x \, m$ and $(x+2) \, m$. If the area of the triangle is $84 \, m^2$,find the lengths of the sides which form the right angle.