I am a beginner, can anyone please help me writing a code for this equation to find 'x' using iteration

I am a beginner, can anyone please help me writing a code for this equation to find 'x' using iteration......

Answer is something approximately 10.59

Answer 1

[Ameer Hamza]

You can use fzero()

eq = @(x) gamma(1+2./x)./gamma(1+1./x).^2 - 1 - (4.56/40)^2;
x0 = 10;
sol = fzero(eq, x0)

Result

>> sol
sol =
   10.5865

Answer 2

[Walter Roberson]

That looks like homework.

syms x
lhs = 1 + sym(4.56)^2/sym(40)^2;
rhs = gamma(1+2/x) / gamma(1+1/x)^2

rhs = 

fplot([lhs-rhs,0], [-20 -5])

fplot([lhs-rhs,0], [-0.75 -0.6])

%fplot([lhs-rhs,0], [-0.5 -0.01])

fplot([lhs-rhs,0], [2.5 20])

There might also be a crossing close to 0, but the plot near there takes too much execution time for me to demonstrate it.