The solar panels you're using produce EU (Industrial-Craft Energy Units), but what the Quarry needs is MJ (BuildCraft Minecraft Joule).
The Electrical Engine is part of the Forestry mod, which is no longer part of Tekkit for some reason or another. It performed that necessary conversion from EU to MJ.
There is another block that does this, though! It's called an Energy Link, courtesy of the Power Converters mod, and it's a bit expensive.
It accepts EU from your solar panels and produces BuildCraft energy. Simply wire it up, and connect it to your quarry. You can place it directly next to the quarry, but if you don't, you need at least two pieces of conductive pipe (wooden, then normal) to connect it.
A quarry needs 22 EU/t to run at full efficiency. However, if you use conductive pipes, the Energy Link will drain a whopping 72 EU/t. I'm not sure if this is a bug, or if it's just that the Energy Link can't tell how much MJ the conductive pipes are going to need. Anyway, you should really place the link directly next to the quarry.
Another thing about it is that you can give the Energy Link a Redstone signal, which makes it stop converting energy. This allows you to turn the quarry on and off (with some delay though, the quarry has an internal energy storage).
(Note that if you're playing Tekkit Lite, this block does not exist. However, you have access to several engines that can indirectly be powered by sunlight. Namely, the 4 different Electric Engines that run off EU – effectively replacing the one from Forestry – and the Blulectric Engine from RedPower that runs off blutricity.)
Remember that RedPower pneumatic tubes will only send items if the source is open, so you can save yourself from overflow with those. Otherwise, for the items with an EMC, condensers are great for collection. For the other items, you could use obsidian pipes leading up to some recyclers, and put the product of that into your mass fabricators (assuming you're using them). You could also just have some obsidian pipes leading to a bunch of chests, and you can go through later and sort out what you need and don't need, or you could have machines do it. In a pinch, if you just want to get rid of waste to prevent lag, lava always works.
Best Answer
It's more reliable to place four land marks in a square. Remember that the maximum quarry size is 64x64, so if your quarry is bigger than that it won't work. Once you've placed your land marks, right click one of them and if they've been placed successfully a red cuboid frame will appear. That will be the frame of your quarry. Next place the quarry down next to any of the land marks. The red frame should change to yellow and black stripes, and all the land marks except one will drop as items (one land mark won't drop, just hit it with your hand and you'll be able to pick it up again). After that, you'll have to supply your quarry with sufficient energy. Quarries can run at any speed up to 5 blocks per second, but a fair amount of power is needed to get them up to a speed at which they can run effectively. You can use either BuildCraft engines (you will need a minimum of three steam or two combustion to run the quarry at a good speed, redstone engines just aren't strong enough) or you can use IndustrialCraft electricity. If you're going to use IC power, you'll need an energy link. Place the energy link directly next to the quarry and connect your BatBox/MFE/MFSU to the energy link with the appropriate cable. Bear in mind that quarries use quite a lot of EU, so you will need a large power source. Sufficient energy is provided by:
You can use water/wind mills to provide power as well, but your quarry will run very slowly if you don't have loads of them. It is best to have the power coming from an MFE or an MFSU because they provide higher voltages and allow your quarry to run faster. Once power is provided to the quarry, wait a few seconds and an orange frame should be built along the yellow and black lines. When the frame is complete, a mining arm should extend down and start to mine blocks. Remember to hook up BuildCraft pipes to your quarry so it can put the mined blocks in a chest.