java编写一个应用程序，在窗口输入a、b、c三个数值，实现ax2+bx+c=0的求解，并将最终的求解的结果在窗口显示出来。

可以使用Swing实现一个简单的GUI程序，代码如下：

import javax.swing.*;

public class QuadraticEquationSolver extends JFrame {
    private JPanel panel;
    private JLabel label1, label2, label3;
    private JTextField text1, text2, text3;
    private JButton button;
    
    public QuadraticEquationSolver() {
        super("Quadratic Equation Solver");
        
        // 初始化组件
        panel = new JPanel();
        label1 = new JLabel("a:");
        text1 = new JTextField(10);
        label2 = new JLabel("b:");
        text2 = new JTextField(10);
        label3 = new JLabel("c:");
        text3 = new JTextField(10);
        button = new JButton("Solve");
        button.addActionListener(e -> solveEquation());
        
        // 将组件添加到面板中
        panel.add(label1);
        panel.add(text1);
        panel.add(label2);
        panel.add(text2);
        panel.add(label3);
        panel.add(text3);
        panel.add(button);
        
        // 将面板添加到窗口中
        setContentPane(panel);
        pack();
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        setVisible(true);
    }
    
    private void solveEquation() {
        double a = Double.parseDouble(text1.getText());
        double b = Double.parseDouble(text2.getText());
        double c = Double.parseDouble(text3.getText());
        double discriminant = b * b - 4 * a * c;
        
        if (discriminant < 0) {
            JOptionPane.showMessageDialog(this, "The equation has no real roots.");
        } else if (discriminant == 0) {
            double root = -b / (2 * a);
            JOptionPane.showMessageDialog(this, "The equation has one root: " + root);
        } else {
            double root1 = (-b + Math.sqrt(discriminant)) / (2 * a);
            double root2 = (-b - Math.sqrt(discriminant)) / (2 * a);
            JOptionPane.showMessageDialog(this, "The equation has two roots: " + root1 + " and " + root2);
        }
    }
    
    public static void main(String[] args) {
        new QuadraticEquationSolver();
    }
}

这个程序使用了JTextField、JLabel和JButton等Swing组件，可以在窗口中输入a、b、c的值，并且点击“Solve”按钮进行求解。当方程有两个实根、一个实根或者无实根时，会在窗口中显示相应的结果。