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.

(N/A) Let the speed of the train be $x \, km/h$.
Time taken to travel $480 \, km = \frac{480}{x} \, hours$.
In the second condition,the speed of the train is $(x - 8) \, km/h$.
It is given that the train takes $3 \, hours$ more to cover the same distance.
Therefore,the time taken to travel $480 \, km = \left( \frac{480}{x} + 3 \right) \, hours$.
Using the relation: $\text{Speed} \times \text{Time} = \text{Distance}$.
$(x - 8) \left( \frac{480}{x} + 3 \right) = 480$
$480 + 3x - \frac{3840}{x} - 24 = 480$
$3x - \frac{3840}{x} - 24 = 0$
Multiplying the entire equation by $x$:
$3x^2 - 24x - 3840 = 0$
Dividing by $3$:
$x^2 - 8x - 1280 = 0$