Range calculation when the variables are not making a symmetric equation

Question

If consider a situation where equations given is not symmetric , that is $a+2b+c = 4$ and $ab + bc +2ca = 8$ , we know the method to find range : that is by making a quadratic , but my query is that here as the equations are not fully symmetric ,so the range we get for a variable say $"a"$ , will it be same range of "$b$" too ? If not how to find the different range of all three , though by intuition we can say range of $a$ and $c$ to be equal as both are similar