MySQL and MSSQL servers are installed on your Web server.

Just take 'localhost' for MySQL and '.\SQLExpress' for MSSQL.
Your Web server address is also the address for your database servers (MySQL/MSSQL)

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Connection String for MSSQL Server
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         connectionString="Data Source=.\SQLExpress;
                                       Initial Catalog=DatabaseNameHere;
                                       User ID=DatabaseUserNameHere;
                                       Password=PasswordHere"
         providerName="System.Data.SqlClient" />




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Connection String for MySQL Server
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         connectionString="Data Source=localhost;
                                       Database=DatabaseNameHere;
                                       User ID=DatabaseUserNameHere;
                                       Password=PasswordHere"
         providerName="MySql.Data.MySqlClient" />