I'll assume you mean 70mg/ml nic base. Remember those "word-problems" we all hated in math class? Here's where they come in handy.
"Zut has 30ml's of 0mg/ml e-liquid. How much 70mg/ml nicotine base should he add so that the resulting mixture is 14mg/ml?"
Now we need to turn this into an equation that we can solve. What are we trying to do? We must add "some amount" of nic base, so that the
amount of nicotine we add, in mg, at 70 per ml, is 14 times the total volume in ml, once we're done adding. We don't know how much "some amount" is, yet, so we'll just call it "x". So to start out, we add "x" number of ml's of nic base, with 70mg of nicotine in each ml, that's x*70 or 70x total nicotine. We'll put that on one side of the equation:
70x = ??
Now, on the other side, we have the finished product. We started with 30ml's, and we added "x" more so there are 30 + x ml's. But we're not talking about ml's of liquid, we're talking about mg's of nic. In each one of those ml's of finished product, there are 14mg's of nic. So the total nic in the finished product is 14*(30 + x). Let's put that on the other side:
70x = 14(30+x)
Great, now we have an equation. The left is how much nicotine there is if you add "x" ml's at 70mg/ml. The right is how much nicotine there is if you have "x" plus 30 ml's at 14mg/ml. All we have to do is solve for x:
70x = 14(30+x)
70x = 420 + 14x
70x -14x = 420 + 14x - 14x
56x = 420
56x/56 = 420 / 56
1x = 420/56
[[ x = 7.5 ]]
You should add 7.5ml of 70mg/ml base to 30ml of 0mg/ml liquid for a total of 37.5ml of 14mg liquid.
Check: 7.5ml * 70mg/ml base = 525mg nicotine added (total, since we started with zero).
525mg / 37.5ml liquid after adding = 14mg/ml concentration in the final product.