But before that, do you distinguish between an equation and its solution? !

The element of the former is an equation, and the element of the latter is a real number.

Also, there are two identical real roots = there is only one solution in the real number range. So the solution of a quadratic equation with the same real root can of course be expressed as a set, and this set has only 1 elements.

As for why there are "two identical real roots", it is after you really embark on the road of mathematics and the undergraduate course develops in the direction of applied mathematics. Here is a simple sentence for you. It doesn't matter if you can't remember:

Any univariate polynomial equation with n complex coefficients (n∈Z+) must have n roots in the complex field. If there are any multiples, count them as multiples!

Therefore, at the beginning, we must declare that the quadratic equation with one variable has two identical real roots, not only 1 real roots (quadratic equation with one variable), in order to conform to this basic theorem.

By the way, this theorem was first put forward by the mathematician Gauss.