How do I make x the subject of this function?

What code do I use MATLAB to make x the subject in the function below?

Y = [D^2 * acos(1-(2x/D)]- [squareroot(x(D-x) * (D-2x)] / [pi*(D^2)]

Where D=0.05m

x=unknown

y=0.2170535

Answer 1

[Piyush Kumar]

@Zaraleena Adamson,

You can use symbolic variables and solve function.

I found this example on the same page -

syms a b c x
b = 2;
c = 3;
x = 3;
eqn = a*x^2 + b*x + c == 0

eqn = 

S = solve(eqn, a)

S = 

I tried for your case, but it is unable to find explicit solution -

syms x D y
% D = 0.1;
% y = 0.2;

% Define the function
Y = (D^2 * acos(1 - (2*x/D))) - (sqrt(x * (D - x) * (D - 2*x)) / (pi * (D^2)));

% Solve for x
solution = solve(Y == y, x);

Warning: Unable to find explicit solution. For options, see help.

% Display the solution
disp(solution);

[Piyush Kumar]

I also tried with fzero to find the roots of the function -

D = 0.05;
y = 0.2170535;

% Define the function
f = @(x) (D^2 * acos(1 - (2*x/D))) - (sqrt(x * (D - x) * (D - 2*x)) / (pi * (D^2))) - y;

% Find a root near an initial guess
initial_guess = D / 2;
solution = fzero(f, initial_guess);

Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at 0.0257071 is -0.21306-0.11966i.)
Check function or try again with a different starting value.

disp(solution);

   NaN

[Torsten]

A plot of the function for 0 <= x <= D/2 says more than a thousand solves ...

Answer 2

[Torsten]

D = 0.05;
Y = 0.2170535;
f = @(X) Y - (D^2 * acos(1-(2*X/D)) - sqrt(X.*(D-X) .* (D-2*X)) / (pi*D^2));
X = 0:0.001:0.025;
plot(X,f(X))

[Walter Roberson]

Note that f(X) is never zero. The equation never reaches 0.2170535 with that D value.

[Zaraleena]

@Walter Roberson @Piyush Kumar Thank you so much for the help.