x_up = 2;
x_down = 1;
error = 0.001;
res_down = x_down^3 - x_down - 1;
res_up = x_up^3 - x_up - 1;

while(res_down * res_up < 0)
        x = 0.5*(x_up + x_down);
        res = x^3 - x - 1;
        
        if( res*res_down < 0 )
                x_up = x;
        else
                x_down = x;
        end

        if( abs(x_up-x_down) < error )
                break;
        end
end

result_x = 0.5*(x_up + x_down)