The distance between two stations is 300km. A train went to second station from first station with uniform velocity. If the velocity of the train had been 5 km / hour more, then the time taken by the train to reach the second station would be lesser by 2 hours.

Explanation

Let the uniform velocity of the second the train be x km/hour.
`:.` the time taken by the second station is `(300)/(x)` hours. If the uniform velform velocity of the train had been 5 km/ hour more, the time taken by the train to reach the second station is `(300)/(x+5)` hours.
As per question, `(300)/(x)-(300)/(x+5)=2`
or, `(150)/(x)-(150)/(x+5)=1or,(150x+750-150)/(x(x+5))=1`
or, `(750)/(x^(2)+5 x)=1or,x^(2)+5x=750`
or, `x^(2)+5x-750=0`.
Hence the required quadartic equation is `x^(2)+5x-750=0`.