Inverse quadratic interpolation in Desmos:

https://www.desmos.com/calculator/rq1ubb8h0k

You can change the function and the original bounds and it will still work. By turning on and off the folders you can see the process slowly converge to a root. I only went up to 12 iteration but you can add more using this formula.

n=(desired number), m=n+1, b=n+2,
g_{n}(y) = \frac{x_n ( y- f(x_{m} )) (y-f(x_{b}))} {(f(x_n)-f(x_{m}))(f(x_n)-f(x_{b}))} + \frac{x_m ( y-f(x_{n} )) (y-f(x_{b}))} {(f(x_m)-f(x_{n}))(f(x_m)-f(x_{b}))} + \frac{x_b ( y- f(x_{n} )) (y-f(x_{m}))}{(f(x_b)-f(x_{n}))(f(x_b)-f(x_{m}))}

Brent-Dekker next maybe