If the value of the discriminant of the quadratic equation $2x^{2} + 5x - k = 0$ is $81$,then $k = \dots$

Find the roots of the quadratic equation by using the quadratic formula:
$-3x^{2} + 5x + 12 = 0$

If the following quadratic equation has two equal and real roots,then find the value of $k$: $(k+1) x^{2}-2(k+3) x+(2 k+3)=0$

Solve the following equation using the method of factorization: $x + 3 + \frac{2}{x} = 0$.

Examine whether the following equation is quadratic or not: $x - \frac{1}{x} = 5$

$120$ 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.