i am a structural engineer analysing a frame. I am trying to find the ponit of maximum bending moment along a beam which is essentially the minimum point on a curve. i am following an example from a text which describe the distance to the max moment using the following expression:

h=(90.9x-4.55x^2)/(10.16+0.4x)

Putting dh/dx=0 he finds an expression from the min point on the curve

The answer is quoted as x^2+50.7x-507.4=0 and then solves for x=8.65

My calculus is rusty but I have tried to differentiate using the quotient rule quoted in maths text books. I cannot replicate this answer; the answer i get is not sensible. Can anyone help?