Is there an equation which allow us to perfectly match a helix propeller and an engine?
Did you try Mark Drela's XROTOR? I have difficulty with your term "helix", but that software should do what you ask if your blade loading is not too high.

From the linked page:
XROTOR is an interactive program for the design and analysis of ducted and free-tip propellers and windmills. 
It consists of a collection of menu-driven routines which perform various useful functions such as:


Design of minimum induced loss rotor (propeller or windmill)
Prompted input of an arbitrary rotor geometry
Interactive modification of a rotor geometry
Twist optimization of an arbitrary rotor for minimum induced loss
Analysis of a rotor with a wealth of choices of operating parameters 
Incoming slipstream effects (from an upstream propeller, viscous wake...)
Multi-point parameter display
Structural analysis and corrections for twist under load
Acoustic analysis with dB noise footprint predictions
Interpolation of geometry to radii of interest
Plotting of geometry, aerodynamic parameters, and performance maps
...