Is there a way to find the values of 3 variables with just one equation? I was doing a personal project until I came upon this equation that i need to solve to continue, the thing is I don’t thing I have been thought this in math ever so i wonder if this even possible to solve at all if why or why not
2850=2x+4y+6z
If i can get more specific, it needs to be real numbers, and cannot be negatives, and must be only integers, no fractions. Can values aside from all real numbers be obtain with those limitations, or is it impossible?
And Thank you for thank you time to answer.

You have a linear equation. That means you have a system of linear equations: a system of $1$ equation and $3$ variables. Because the number of variables is greater than the number of equations, the system is underdetermined. That means the system has infinitely many solutions.
But you are asking only for the non-negative integers.
$\ $
$$2850=2x+4y+6z$$
$$1425=x+2y+3z$$
Because you are asking for non-negative integers, you are asking for integer partitions of 1425.
You need a calculation software for that.
a)
You can use an algorithm that generates all $113072609699904337559514844445146843472$ partitions of $1425$ and write a small algorithm for extracting the wanted partitions.
b)
Here is a Maple code for generating only the wanted partitions:
$\text{n:=1425:}$
$\text{add(add(x^(n-2*j-3*k)*y^j*z^k,j=0..(n-3*k)/2),k=0..n/3);}$
Because the number of partitions is too large, you should split the command, e.g. into steps of $100$:
$\text{add(add(x^(n-2*j-3*k)*y^j*z^k,j=0..(n-3*k)/2),k=0..100);}$
$\text{add(add(x^(n-2*j-3*k)*y^j*z^k,j=0..(n-3*k)/2),k=101..200);}$
...
$\text{add(add(x^(n-2*j-3*k)*y^j*z^k,j=0..(n-3*k)/2),k=401..475);}$
You can translate that e.g. into the language of SageMathCell.
c)
You can write that in a loop algorithm.
Here is a Maple code:
$\text{n:=1425:}$
$\text{for k from 0 to n/3 do}$
$\text{ for j from 0 to (n-3*k)/2 do}$
$\text{  x^(n-2*j-3*k)*y^j*z^k:}$
$\text{print(%):}$
$\text{ od:}$
$\text{od:}$
You can translate that e.g. into the language of SageMathCell.
