Solving circuit design problem with two approaches
The flaw is that this equation has some restrictions when applied to a real circuit. From a mathematical perspective the second solution is correct. But as still applied that

\$Ra=500\Omega-Rb\$ 

you would end up with a negative resistance for 

\$Ra = -1579\Omega\$ 

In the real world such a thing doesn't exist and therefore the solution is not applicable for your problem.