Solving 3 nonlinear equations

Hi people,
I am new here. Actually I find here while searching for something but I liked this active forum and I wanted to be a part of it 😁

Actually I wasn't here for this question but since I am here, I want to ask you something.

For a personal project of mine, I need to solve three 2nd degree 3 unknown equations. The project is something like finding position of an object with a camera (I am trying some new thing, if it works, I will give detail or maybe some videos here 😁)

The equations are like
x^2+5y^2+3z^2 = 653 (three of theese equations)

I tried to solve with matlab and it gives 8 solutions for every one of the parameters (x, y, z). Actually 2 of the solutions are positive real numbers, 2 of them are negative of theese 2 real numbers and four complex numbers which have different + - configurations.

I only need those 2 positive real numbers. But I need to solve this eqn. set in C# (since my project is in C#). I can't use iterative methods because they stop when they find a value. But I need both of these 2 positive real solutions.

Do you have any idea?

Thanks already 😀