Fundamental equations in economics For the other sciences it´s easy to point to the most important equations that ground the discipline. If I want to explain Economics to a physicist say, what are considered to be the most important equations that underly the subject which I should introduce and attempt to explain?
Instead of proposing specific equations, I will point to two concepts that lead to specific equations for specific theoretical set ups:

A) Equilibrium
The most fundamental and the most misunderstood concept in Economics. People look around and see constant movement -how more irrelevant can a concept be, than "equilibrium"? So the job here is to convey that Economics models the observation that things most of the time tend to "settle down" -so by characterizing this "fixed point", it gives us an anchor to understand the movements outside and around this equilibrium (which may be changing of course).

It is not the case that "quantity supplied equals quantity demanded" (here is a foundational equation)  

$$Q_d = Q_s$$

but it is the case that supply tends to equal demand (of anything) for reasons that any economist should be able to convincingly present to anyone interested in listening (and deep down they all have to do with finite resources).

Also, by determining the conditions for equilibrium, we can understand, when we observe divergence, which conditions were violated. 

B) Marginal optimization under constraints
In a static environment, it leads to the equation of marginal quantities/first derivatives of functions.
Goods market: marginal revenue equals marginal cost.
Inputs market: marginal revenue product equals marginal reward (rent, wage).
Etc. (I left "utility maximization" out of the picture on purpose, because, here first one would have to present what this "utility index" is all about, and how crazy we are (not), by trying to model human "enjoyment" through the concept of utility).  

Perhaps you could cover it all under the umbrella "marginal benefit equal marginal cost" as other questions suggested:

$$MB = MC$$

Economists live in marginal optimization and most consider it self-evident. But if you try to explain it to an outsider, there is a respectable probability that he will object or remain unconvinced, instead usually proposing "average optimization" as "more realistic", since "people do not calculate derivatives" (we don't argue that they do, only that their thought processes can be modeled as if they were). So one has to get his story straight about marginal optimization, with convincing examples, and a discussion about "why not average optimization".

In an intertemporal setting, it leads to the discounted trade-off between "the present and the future", again "at the margin" -starting with the "Euler equation in consumption", which in its discrete deterministic version reads

$$u'(c_{t})=\beta(1+r_{t+1})u'(c_{t+1})$$

...and one cannot avoid the theme of utility, after all: $u'()$ is marginal utility from consumption, $0&lt;\beta&lt;1$ is a discount rate and $r_{t+1}$ is the interest rate

(don't consult wikipedia article on Euler's equation in consumption, the concept behind it is much more generally applicable and foundational than the specific application that the wikipedia article discusses).  

Interestingly, although dynamic economics are more technically demanding, I find this more intuitively appealing since people seem to understand way better "what you save today will determine what you will consume tomorrow", than "your wage rate will be the marginal revenue product of all labor employed".