a=2

b=3

c=7

d=5

w=14 

 Find x using newton raphson method in matlab 

enter code here 

4.w.d^2.(1-x^2)^2=a.b.c^3.x.sqrt(pi^2.(1-x^2)^2+16.x^2) 

Answer: 

There is a ton of posts similar to this, even on StackOverflow, like this one, or this one. Even more on the web like Matlab Central, or other educational sites like here. So, I think you could have come to the table a little more prepared. I'll put my two cents in here as far as the method I like the best. 

 function x = newton(f,dfdx,x0,tolerance)
err = Inf;
x = x0;
while abs(err) > tolerance
   xPrev = x;
   x = xPrev - f(xPrev)./dfdx(xPrev);
   % stop criterion: (f(x) - 0) < tolerance
   err = f(x); % 
   % stop criterion: change of x < tolerance
   % err = x - xPrev;
end

f = @(x) ((x-4).^2-4);
dfdx = @(x)(2.*(x-4));
x0 = 1;
xRoot = newton(@f,@dfdx,x0,1e-10);

f(x) = 4wd²(1-x²)² - abc³x√(π²*(1-x²)²+16*x²)

So just differentiate the above equation with respect to x and then you have your df/dx. Plug the equations into the file handles and run the routine! Also, I'm fine with moving this to SE Math, but I don't know how to do that either. :-)