One host, two blogs?

Hey there! I have a domain name and all, but I was wondering if it’s possible to run two blogs under the same host? For example, my main blog would be: https://www.mainblog.com, while my second blog would be like: https://www.mainblog.com/otherblog. I’ve tried to install wordpress and stick it in a new directory, but then I ran into problems when I came to the install.php part. Should I keep fooling with it or just give up if it isn’t possible?

OH, also, my page’s links turned all blue, if it’s not too much trouble, I’d like to know why that is. Nothing changed in my CSS codes. :/ Thanks for reading!