This formula is used to find out whether the roots of the quadratic equation are real or imaginary. The discriminant calculator is a free online tool that gives the discriminant value for the given coefficients of a quadratic equation.The discriminant tells us whether the solutions are real numbers or complex numbers as well as how many solutions of each type to expect. ⓑ using the Quadratic Formula. The standard form of a quadratic equation. By completing the square method, add b2 on both sides. The solution set is {4±2 √3}. The term under the square root i.e. Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation. What is a Quadratic Equation?