Why do we seek for the $x$ where $f(x) = 0$? I'm studying numerical analysis on college, and a question that has been following me (since I've started studying calculus) is why do we seek for the $x$ value where $f(x) = 0$? Can someone exemplify a real situation where this would be important? Because all I've seen are approaches to try to find this $x$ value, but I still don't understand why we are trying to find it.
Thanks in advance :)

As Robert Israel mentioned in the comments, you can solve $A(x)=B(x)$ by defining $f(x)=A(x)-B(x)$ and solving for $f(x)=0$.
A classic example of this would be finding the square root of a number: suppose we want to find $\sqrt5$, say. Then we're looking for $x$ where $x^2=5$. Let $f(x) = x^2-5$. Now you can use Newton's method (for example) to solve for $f(x)=0$.
