$120$ kites were divided equally among a certain number of children in a school. If there were $4$ children fewer,each child would have received $1$ kite more. Find the number of children.

Obtain the roots of the following quadratic equation by using the general formula for the solution: $25x^2 + 20x + 7 = 0$.

Find the discriminant of the following quadratic equation and hence determine the nature of its roots: $x^{2}-2 \sqrt{2} x+1=0$

State whether the quadratic equation $2 x^{2}-6 x+\frac{9}{2}=0$ has two distinct real roots. Justify your answer.

Examine whether the following equation is quadratic or not: $7x = 2x^2$.

The speed of the flow of a river is $3 \, km/hr$. $A$ motorboat goes $12 \, km$ downstream and comes back in a total time of $3$ hours. Find the speed of the motorboat in still water. (The speed of flow of water is less than the speed of the boat.)