Examine whether the following equation is quadratic or not: $x^{2}-3=\frac{2}{x}$

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

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

Represent the following situation in the form of a quadratic equation:
$A$ train travels a distance of $480 \, km$ at a uniform speed. If the speed had been $8 \, km/h$ less,then it would have taken $3 \, hours$ more to cover the same distance. We need to find the speed of the train.

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $2 y^{2}+5 y-3=0$.

$A$ car takes $60$ minutes less for a journey of $150\,km$,if its speed is increased by $5\,km/hr$ from its usual speed. Find the original speed of the car in $km/hr$.