No, you can't run guitars direct to a mixer without exploding your speakers. You need the guitar amp to balance out the signal before running them thru a mixer. Keyboards no problem running direct.
I'm sorry, but you are absolutely wrong. And I apologize to everyone for going off topic, but being a guitar player for over 30 years, and having been in more working bands then I care to count, and having played hundreds of paying gigs, and having owned, used and understood thousands of $ of sound reinforcement equipment over the years, and having an electronics background, I'm not going to be told I'm wrong, when in fact, I'm quite right.
You
can plug a guitar directly into a mixing board. I've done it. Many times. I've never "shattered" or "exploded" a speaker. Most electric guitars manufactured and played have high impedance pickups. Mixers have low impedance input. This mismatch in impedance causes the signal from the guitar to be "loaded down", ie., it kills the voltage of the incoming signal. The output (sound level) coming out of the speakers will be very low, making it incredibly difficult to blow your speakers. There will also be a huge loss in dynamics and your guitar will sound very thin and tinny. A pre amp matches the impedance, thus effectively boosting your signal.
Guitars and basses with active pickups (battery powered) are low impedance devices, as is the line out on an electronic keyboard. This is why they can be plugged directly into a mixer. There is no impedance mismatch and the signal suffers no "loading down" and provides a nice hot, useable signal to your power amp. You would be far more likely to blow your speakers this way, but that's why you have a mixer to regulate the voltage level. A pre amp isn't required in this situation, but if you want precise tonal control of your sound, you'll use one.
As far as "balancing" the signal, I can only assume you're confused about what a balanced input on a mixer is. It has nothing to do with signal strength. A high impedance device using a high impedance cable, will pick up noise on its way to the destination source (mixer). The longer the cable, the more noise it will pick up. Not a desireable thing on stage or in the studio. A balanced input (bal) almost completely eliminates this problem, therefore very long cable runs can be used with virtually no noise being picked up along the way. It neither increases nor decreases signal strength, it simply eliminates hum.
This is what you can do; from your posts, I'm thinking you have access to a mixer. If so, plug your keyboard into the channel of your choice. Have the monitor out level for that channel all the way down. Run a cable from the monitor out of that channel into your camera. Adjust the monitor out level until your recorded signal sounds good and isn't clipping the amp in the camera. Cameras and cam corders, etc., record at a fixed level. Running your keyboard directly into the cam is providing a signal that's way too hot for the preset record level of the camera. You need to kick it down.