Since there are x students in the class, each student must have been (x - 1) classmates.

To see this, pretend you are a student in a classroom of size 40.

You will have 39 classmates.

Classmate A will have 39 classmates including you.

Classmate B will have 39 classmates including you and A.

Classmate C will have 39 classmates including you, A and B.

And so on.

Add that to the two form teachers and each of the x students would have bought (x + 1) presents.

Since the total number of presents bought is 1640 and each of the x students in the class buys (x + 1) presents,

x (x + 1) = 1640
x2 + x = 1640
x2 + x - 1640 = 0

which is in the form ax2 + bx + c = 0 where a = 1, b = 1 and c = -1640.

"Do not evaluate" just simply means you are nor required to solve the quadratic equation formed, which would have gone

(x + 41) (x - 40) = 0
x + 41 = 0 or x - 40 = 0
x = -41 or x = 40

indicating that there must have been 40 students in the class.

Still unable to get understand sorry

You must imagine this scenario from each student's perspective.

Each of the x students in the class would see (x - 1) other people being present in the class.

TQ sir!

So if there is indeed 40 students in the class, this is what happens.

Student A buys presents for 39 classmates and 2 teachers.

Student B buys presents for 39 classmates and 2 teachers.

Student C buys presents for 39 classmates and 2 teachers.

Student D buys presents for 39 classmates and 2 teachers.

And so on.

In any case, each of the 40 students buys 41 presents.

In this question, the number of students is x. Similar idea applies. Remember that a student does not buy a present for himself/herself.