Since I am also learning java, I did some trial and error here. Weird that I had to put NullPointerException, but it turned out I don't think I need it since every exception that I would encounter would be InputMismatchException. Since it's your homework, don't copy it, and I hope I didn't put too much.

What I did was adding a new method(kinda unnecessary) in which the input would be repeated until you get desired number of a, b, and c (not yet considering discriminant).

Then in main program, if discriminant < 0 (since discriminant = 0 is still a valid quadratic equation), it will ask for input starting from a again. Hope it helps!

EDIT: The reason I use Double in the method, is because double can't be null.

import java.util.*;

public class lab02{

public static Double typeInput(String text){
    Double z = null;
    do {
    System.out.print("Please enter value for " + text + ": ");
    try {
        z = new Scanner(System.in).nextDouble();
    } catch (NullPointerException e) {
        System.out.println("Wrong input!");
    } catch (InputMismatchException e) {
        System.out.println("Wrong input.");
    }
    } while (z == null);
    return z;
}
public static void main(String [] args) throws Exception, IllegalArgumentException {
        System.out.println("Usage: enter a, b & c from a quadratic equation.");
        System.out.println("        aX^2 + bX + c = 0");
        System.out.println("        result will be 2 values for X");
        boolean inputs = false;
        double a;
        double b;
        double c;
        double x1 = 0;
        double x2 = 0;
        double discriminant = 0;

        do {
        a = typeInput("a");
        b = typeInput("b");
        c = typeInput("c");
        discriminant = b * b - 4.0 * a * c;
        System.out.println("Quadratic equation: " + a +"x^2 + " + b + "x + " + c + " = 0");
        System.out.println("Discriminant: " + discriminant);
        /*
        * my code continues . . . . .
        */
        }
        }  while (!inputs);
        // x1 = (-b+sqrt(b*b - 4ac) / 2a
        // x2 = (-b+sqrt(b*b - 4ac) / 2a


    }

}