The discriminant tells us how many solutions the quadratic has. B 2 4ac 0. The means there are TWO answers.
Displaystyle left x frac b 2aright 2 frac b 2-4ac 4a 2.
It can easily be seen by polynomial expansion that the following equation is equivalent to the quadratic equation. To understand it to value it and to apply it correctly you need to know a tiny bit of its background then appreciate every term in it. Displaystyle left x frac b 2aright 2 frac b 2-4ac 4a 2. When you simplify using the quadratic formula and your result is a negative number under a square root there are no real number solutions to the equation.