how to solve an equation iteratively?

I need to solve the following equation and get a real number:

Below are my codes. When doing this, the solution returned are all complex values. How can I iteratively solve this equation such that x can be a real number? I already know the correct solution is about 7.78016, but I need to reproduce the procedure

syms x
eqn1 =200 == x*(1-(0.4*(x-1))/sqrt(2.8*2.4*x+0.4))^(-2.8/0.4);
sol = solve(eqn1,x) 

Answer 1

[Walter Roberson]

syms x
eqn1 =200 == x*(1-(0.4*(x-1))/sqrt(2.8*2.4*x+0.4))^(-2.8/0.4);
sol = solve(eqn1, x);
sol = sol(imag(sol) == 0)

sol = 

vpa(sol)

ans = 

7.7212920018186473025078617929192

[Randy Chen]

thank you!