Have you ever heard of a computer algebra system (CAS)? It's the generic name for software that performs symbolic mathematics, anything from the algebra that 8th graders are taught to differential equation solvers used in modern physics research. http://en.wikipedia.org/wiki/Computer_Algebra_System
The specifics don't matter, the bottom line is, anything that Mathematica can solve, this can be useful for, simply by solving the equation for the chosen dependent variable (the red number) every time you adjust the value of an independent variable (any of the black numbers).
Firstly, if that's how this works -- rather than by allowing you to guess and check until things match up -- then I am very much misunderstanding it. Secondly, there's no way this thing is going to be as powerful as a CAS. Hell, from the description I seriously doubt it'll do so much as solve a system of linear equations for you, just let you explore the space until you find a solution.
One of us is misunderstanding something. What I'm imagining is, you adjust the value by dragging it, and then the CAS solves for the red value. There's no requirement for monotonicity or anything, if the CAS can solve for a unique red value to satisfy the equation, you're good.
The specifics don't matter, the bottom line is, anything that Mathematica can solve, this can be useful for, simply by solving the equation for the chosen dependent variable (the red number) every time you adjust the value of an independent variable (any of the black numbers).