I have been given the equation $M=Wx\frac{l-x}{2}$
- $M$ is the Bending moment
- $W$ is the Weight per unit length
- $L$ is the Length
- $x$ is the distance of load from one end.
I have found the derivative $f(x) = \frac{Wl}{2} - Wx$
I am unsure where to go from here. The examples which I have found online don't give three unknowns.
From what I understand I need to make this equation equal zero and then solve for x to determine my maximum but how would I solve for $x$ with 3 unknowns?
You took the derivative and now you have to set it equal to zero. That allows you to solve it for $x$. It follows that $W$ is independent here for your solution, $x$ will depend on $l$ only. Alternatively your formula is of quadratic nature, a parabola that opens down. So you can find the desired value of $x$ by using the well known formula $-b/(2a)$ from your algebra class to find the same result. Side note, there is only one unknown which is the $x$. The other letters are assumed fixed parameters. Either way, you should find $x=l/2$ but I want you to verify that.