The formula for the discriminant is simple but powerful: D=b2−4ac. The discriminant is an important term to know when dealing with quadratic equations.Essentially, the discriminant is simply this expression: b2-4ac. The discriminant is defined as Δ=b2−4ac. This is the expression under the square root in the quadratic formula. The discriminant tells you about the "nature" of the roots of a quadratic equation given that a, b and c are rational numbers. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. The formula derives from the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Moreover, the discriminant tells how many solutions to the equation there are as well as if the solutions are real or imaginary.