finding roots (Max Like Est)

I have this maximum liklihood estimate problem

i need to find the roots of the following:

[sum (from i=1 to n) ] ((2(x[i]-parameter)/(1+(x[i]-parameter)^2))=0

given to me is the x vector which has length 100

how would I find the roots using R? 

I have 2 thoughts...... 1 is using a grid search ... eg. brute force, just
choosing a whole bunch of different values for my parameter .... such as
parameter=seq(0,100,.1) .... and this is what I have so far, 

	john=rep(0,length(x))
	for(i in 1:length(x)) {
	john[i]=((x[i]-0)/(1+(x[i]-0)^2))
             }
             sum(john)

then 

	john=rep(0,length(x))
	for(i in 1:length(x)) {
	john[i]=((x[i]-.1)/(1+(x[i]-.1)^2))
             }
             sum(john)

then 

	john=rep(0,length(x))
	for(i in 1:length(x)) {
	john[i]=((x[i]-.2)/(1+(x[i]-.2)^2))
             }
             sum(john)

something like this ... 

             theta=seq(0,100,.1)
	john=rep(0,length(x))
	for(i in 1:length(x)) {
	john[i]=((x[i]-theta[j])/(1+(x[i]-theta[j])^2))
             }
             sum(john)

but something is wrong with my code because its not working. Anyone have any
ideas? (I am very new to R and statistical software in general)

The 2nd thought was to use the Newton Raphson Method, but, I dont even know
where to start with that. 

Any thoughts help. 

Thanks