When would I use the Quadratic Formula? We need to make one side of the equation zero before we can apply the quadratic formula.Today we're going to use the discriminant to determine what kind of roots we have for this quadratic equation. The discriminant is positive, so there are two real solutions. The formula derives from the quadratic formula. The discriminant won't tell you what the roots or Solutions of your quadratic equation are but they will tell you what kind of roots they are. Formula for Discriminant. The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant in math is defined for polynomials and it is a function of coefficients of polynomials.