The quadratic equation has many application related to resolving and modelling daily life problems. two examples are in Archery and rifle sports. The trajectory of the projectile can follow a ballistic arc. The arc itself can be explained and graphically illustrated by the quadratic equation.
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The question is based on the false assumption that the quadratic formula is not used in daily life. Wrong, it IS!
Quadratic equations doesn't help you in life specifically. It just combines a bunch of different math properties. It helps to focus your brain, gain concentration and intellect.
How about the distance travelled when you are accelerating at a constant rate? eg falling under the influence of gravity?
Anything involving a square law automatically invokes a quadratic function by definition, even if the equations is as simple as y = x^2, such as the area of a square (hence the names). At a more advanced level, quadratic and higher-order functions crop up in all manner of real-life science and engineering problems.
Convention says that they are quoted as being equal to zero. It makes life FAR easier that way.