Check whether the following is a quadratic equation:
$x^{2}-2x=(-2)(3-x)$

Check whether the following is a quadratic equation:
$x(2x + 3) = x^2 + 1$

Check whether the following is a quadratic equation:
$(x-2)(x+1)=(x-1)(x+3)$

Represent the following situation in the form of a quadratic equation:
The product of two consecutive positive integers is $306$. We need to find the integers.

Find the roots of the following equation:
$x + \frac{1}{x} = 3, x \neq 0$

$A$ motor boat whose speed is $18\, km/h$ in still water takes $1\, hour$ more to go $24\, km$ upstream than to return downstream to the same spot. Find the speed of the stream. (in $ km/h$)