Manipulating the centered difference approximation

AI Thread Summary
The discussion centers on a mathematical problem involving the centered difference approximation, specifically showing the equivalence of two equations. The poster struggles to manipulate the equations and seeks assistance, particularly from those with expertise in atmospheric or meteorological studies. They suggest treating the equation as a quadratic form, a*x**2 + b*x + c = 0, and solving for x. Clarification is needed regarding the placement of the radical sign over the division by R. Overall, the thread highlights a request for guidance in resolving a complex mathematical equation.
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The equation is attached in the image file. I tried several times to work it out but I can't figure this out for the life of me. They just want me to show that the first equation equals the second one. Any atmospheric/meteorology majors out there? Any help in general would be appreciated.
 

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Treat it as a*x**2 + b*x + c = 0 and solve for x. The radical sign should extend over the division by R.
 
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