Router WiFi with solar energy
I'm going to assume that your router uses about 7W, as measured on a similar router.

If you don't consider inefficiencies then the math works like this:

Nominal battery power rating: \$12 V \times 30 Ah = 360 Wh\$

Dividing by your consumption: \$\frac{360 Wh}{7 W} = 51.4 hours = 2.1 days\$

But there are inefficiencies.  I assume you are connecting the battery to an inverter, then the inverter to the router's power supply.  Each of these conversions wastes energy.  If each conversion is 85% efficient, then you get a combined inefficiency of \$0.85 \times 0.85 = 0.7225\$.  This means that the entire system is 72.25% efficient.

So, multiplying it out: \$51.4 hours \times 0.7225 = 37.1 hours = 1.55 days.\$

This should be fairly realistic, although you may want to verify the values (router power, inverter inefficiency, etc)

Note that this figure is simply based on a full battery. It doesn't consider the amount of power provided by the panels. We would need a lot more information to try to predict the power generated by the solar panel.