how to solve an equation iteratively?

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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)

Accepted Answer

Walter Roberson
Walter Roberson on 24 Feb 2021
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

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