Lixin has x number of classmates and plan to buy her a birthday gift worth $36.
So basically, they need to contribute 36/x dollars each in order to buy the gift.
But 5 of them will not contribute and it cost them to add $0.24 each
So from 36/x dollars, it become (36/x + 0.24) dollars each
Multiply this individual contribution by the number of her classmates which was reduced by 5. (x - 5)
The equation will be :

Simplify the equation :

Multiply both sides by x to remove the denominator.

Rearrange and combine like terms :

Divide both sides by 0.24 to make the coefficient of x^2 become 1 :

Solve by factoring completely :

Equate both factors to 0, then solve for x :
x - 30 = 0
x = 30
x + 25 = 0
x = -25
Neglect negative value since there is no negative value for the number of persons.
The answer is x = 30
To summarize :
i Expression in terms of x :

ii Equation in x that reduces to x^2 - 5x - 750 = 0

iii Number of classmates Lixin has.
x = 30