I think to answer this question, we will need to dive into physics and aerodynamic theory. All of this information is coming from William Kershner's book The Advanced Pilot's Flight Manual, 6th edition. I am not familiar with with your formulas stated above but will give you how Vx and Vy are calculated.

In America, we typically talk about a force in pounds. The rest of the world use Newtons to describe a force. We can apply a force on a brick wall (that doesn't move) and break a sweat but no work has been done. work is defined as a force * distance. The amount of work accomplished has nothing to do with time. Power is more useful and adds a time-frame element. Thus Power = Work / time. The most common measurement of power is Horsepower and HP = 550 * power (in American measurements).

Thrust Horsepower (THP) can be defined as the amount of force exerted to move an object at a certain rate (time).

Brake Horsepower (BHP) can be defined as the amount of "force" created in the engine before it is transferred to the propeller.

It would go to reason that the airplane will always create more BHP than THP. BHP is efficiency of the airplane engine after frictional loss. This BHP is transferred to the propeller where part of it is transferred to THP. The loss of "force" is due to propeller efficiency.

Thus THP = BHP * propeller efficiency.

If we were to draw out the BHP and THP required curves, it will look a whole lot like the total drag curve of the airplane. Thus at slower airspeeds more BHP/THP is required till it drops to a minimum at some airspeed and then BHP/THP starts to increase to the maximum speed of the airplane.

The THP available curve typically increases as the speed increase in upside down parabolic fashion where the vertex of the parabola is at the max speed. The BHP available curve looks pretty constant for any airspeed but definitely has some curvature.

To find out what speed Vy is we will need to determine the maximum difference between the THP required and THP available. The airspeed at which the difference between THP available and THP required is at a maximum is Vy. This speed is our best rate of climb speed (best time to altitude)

The same process is used for Vx. We take the maximum difference between the BHP required and available curves and that specific speed is our best angle of climb speed. (shortest distance to altitude)

If we go back to our definitions of THP and BHP. BHP is work (force * distance) and is best used for max climb with shortest distance or Vx airspeed.

Thrust Horsepower has a time element associated with it which is power (Work / Time). This difference is important as excess power is what makes an airplane climb in minimum time or Vy airspeed.

CL/CD is the speed where drag is a minimum. This doesn't guarantee that this speed is where the greatest difference is between BHP available / required curves.

As an airplane climbs in altitude, Vy (indicated airspeed) will decrease and Vx (indicated airspeed) will climb. At some altitude, these two speeds will meet. This altitude is known as the absolute ceiling of the airplane.