Question

why do we use symbols

Answer 1

Symbols were indeed introduced for convenience reasons. Because of them we can write math and perform computations on paper much faster than if we had to use words. Try writing the quadratic formula or the law of cosines entirely in words and you will see if your friends can figure out what the resulting sentences mean. They will likely be confused for a while.
As for the reasons for particular symbols, to make them easy to remember.

Answer 2

For making things easy to recognise