Why can’t you use the quadratic formula for every quadratic?

For most Quadrátics in the form of ax^2+bx+c=0there is atleast 2 solutions in most cases as the graph of the quadratic passes the x axis on most cases. But In some cases the quadratic graph doesn’t Cross the x-axis which means that when you equate it to 0 there is no real solutions and the quadratic formula will be undefined as the square root part will be negative of the quadratic formula which is not defined unless stated that you are working on complex numbers.