How do you root without a PC? You don't, and those automatic rooting apps you mentioned are known to install spyware into the phone. Because they are making system level changes, the spyware is difficult to remove.
And that's how those apps are free. Have to pay their developers somehow.
Your device isn't really a known brand either, which means it's unlikely anyone has gone through the effort to put out manual rooting info. Your best bet is to try the XDA Developers site, as they focus a lot of that sort of thing, but I wouldn't get my hopes up.