Originally you have 3.5 gallons of acid and 3.5 gallons of water.  In the final solution, you want those 3.5 gallons of water to be 20% of the total liquid.  The total amount of liquid (100%) is therefore 5 x 3.5 (because 100% = 5 x 20%).  5 x 3.5 = 17.5 gallons.

We want 80% of those 17.5 gallons to be acid.  80% of 175 is 0.8*17.5=14.0.  We already had 3.5 gallons of acid, so we need to add 14-3.5 = 10.5 gallons more.

The answer is 10.5 gallons.