Soluciona Ecuaciones de 2do Grado... contiene un modulo el cual cree especialmente para esta ocasion.

Modulo Ec2Solver

Module Ec2Solver
    '*----------------------------------------------------------------------------------------------*
    '| Author: [L]ord [R]NA                                                                         |
    '| Country: Dominican Republic                                                                  |
    '*----------------------------------------------------------------------------------------------*
    ' Description: A Module to solve 2nd Degree Equations. The Module Ec2Solver has a Function that |
    ' Get the First 3 constant value of the equation And 2 Double Variables are public in the module|
    ' to get the possible values of X. If everything is Ok the Function return True and if it's     |
    ' something wrong Return False.                                                                 |
    '*----------------------------------------------------------------------------------------------*
    '|Website: http://lordrna.co.cc/ http://foro.h-sec.org/                                         |
    '|Mail: lordrna@h-sec.org                                                                       |
    '*----------------------------------------------------------------------------------------------*
    Public X1 As Double, X2 As Double
    Dim A1 As Double, B1 As Double, C1 As Double
 
    Public Function Ec2Solver(ByVal A As String, ByVal B As String, ByVal C As String) As Boolean
        If Double.TryParse(A, A1) And Double.TryParse(B, B1) And Double.TryParse(C, C1) Then
            Ec2Solver = Ec2Solver(A1, B1, C1)
        Else
            Ec2Solver = False
        End If
    End Function
 
    Public Function Ec2Solver(ByVal A As Double, ByVal B As Double, ByVal C As Double) As Boolean
 
        Dim temp As Double
        X1 = 0
        X2 = 0
        If A = 0 Then Ec2Solver = False
        If B = 0 And A <> 0 Then
            If C / A > 0 Then
                Ec2Solver = False
            Else
                If C = 0 Then
                    Ec2Solver = True
                Else
                    X1 = -System.Math.Sqrt(System.Math.Abs(C / A))
                    X2 = System.Math.Sqrt(System.Math.Abs(C / A))
                    Ec2Solver = True
                End If
            End If
        ElseIf C = 0 Then
            X1 = B / A
            Ec2Solver = True
        Else
            temp = (System.Math.Pow(B, 2)) - 4 * A * C
            If temp < 0 Then
                Ec2Solver = False
            Else
                temp = System.Math.Sqrt(temp) / (2 * A)
                X1 = -B + temp
                X2 = -B - temp
                Ec2Solver = True
            End If
        End If
 
    End Function
End Module
 

Source

Public Class Form1
 
    Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        A.Clear()
        B.Clear()
        C.Clear()
        X1.Clear()
        X2.Clear()
    End Sub
 
    Private Sub A_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles A.Click
        A.Text = ""
    End Sub
 
    Private Sub B_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles B.Click
        B.Text = ""
    End Sub
 
    Private Sub C_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles C.Click
        C.Text = ""
    End Sub
 
    Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click
        If Len(A.Text) = 0 Or A.Text = "0" Then A.Text = "1"
        If Len(B.Text) = 0 Then B.Text = "0"
        If Len(C.Text) = 0 Then C.Text = "0"
 
        If Ec2Solver.Ec2Solver(A.Text, B.Text, C.Text) = True Then
            X1.Text = Str(Ec2Solver.X1)
            X2.Text = Str(Ec2Solver.X2)
        Else
            X1.Text = "Sin Solucion"
            X2.Text = "Real"
        End If
    End Sub
End Class