normal distribution as question

attempted a question and the answer given is oddly not what i got even though I went over the question again with a revision book.
question is:
x~n(20,12)
find the value of a such P(X < a) = 0.40
so I converted 0.40 to 0.6554 using the normal distribution table.
so the equation will be:
(a-20/(root12)) = 0.6554
so it will simplify to a*(root12)+20 which would give A.
The answer is actually 19.1....
even if I did something wrong I do not see how this is the right answer as you have to plus 20 so it will always be bigger than 19.1... followed the revision guide and still cant get it so I was hoping the wonderful community of tsr could help me?

Thanks for the help!! I have a terrible maths teacher who often jumps to the equations before explaining what each variable means which is obviously very very stupid and annoying. So just to clarify, if you don't mind me asking, what is Z, z, a or a and b and what does the formula x-mean/standard deviation actually work out and if you don't me asking as well, why does the equation do that? Revision book is crap for this topic for some reason..

Z represent the random variable of the standardised normal distribution N(0,1), which you can find in tables.

z refers to values it takes.

There's no specific meaning to a,b in reference to the normal distribution.

If X is a random variable with distribution $N(\mu,\sigma^2)$ then $\dfrac{X-u}{\sigma}$ has distribution N(0,1), and so can be looked up in tables.

Oh thanks Would you be able to write out the equation for a if you don't mind, I learn better from examples to see how it works.