$x = \dots$ is a solution of the quadratic equation $x^{2} + 7x + 12 = 0$.

Find two numbers whose sum is $27$ and product is $182$.

One of the solutions of the quadratic equation $(x-3)^{2}-4=0$ is ..... .

Find the roots of the following quadratic equation by factorisation:
$x^{2}-3x-10=0$

Solve the following equation using the method of factorization: $6(2x+1)^2 - (2x+1) - 5 = 0$

The diagonal of a rectangular field is $60\, m$ more than the shorter side. If the longer side is $30\, m$ more than the shorter side,find the sides of the field. (in $m$)