Code:y = sqrt[(((85/x) * 85 - x^2)/ x) ] = ((85^2/x) + x^2)/ 85 In[27]:= p = ((85/x) * 85 - x^2)/ x - (( 85^2/((85^2/x) + x^2) ) ^2); sol = NSolve[p == 0, x] Out[28]= {{x -> -36.2894}, {x -> 27.7376 + 21.7226 I}, {x -> 27.7376 - 21.7226 I}, {x -> -10.093 + 32.5167 I}, {x -> -10.093 - 32.5167 I}, {x -> 9.44493}, {x -> 0.257048 + 9.23565 I}, {x -> 0.257048 - 9.23565 I}, {x -> -8.95875}} This is still an approximation. In the above example 9 solves the equation better than 5. That is where 5 should be the desired answer. N = 85; x = 5; and y = 17 . So there still isn't a perfect solution just estimated. But take: In[31]:= y = sqrt[(N * y - x^2) / x] y = sqrt[(7872197 * 3191 - 2467^2) / 2467] Out[31]= sqrt[(-x^2 + N sqrt[(-x^2 + N sqrt[(-x^2 + 1/85 N (7225/x + x^2))/x])/x])/x] Out[32]= sqrt[10180014] So sqrt of 10180014 = 3190.613421 which is approx y or 3191. So y and p equations above hold true. But the problem is it is still an approximation. But Calculus can be used to determine where the graph approaches a correct value.