Solution of a nonlinear system of equations with 3 unknowns

Question

How do I most elegantly solve the equation system?

$\begin{array}{|l l} B= 2a^2-b^2+2c^2 \\[0.75em] C = 2a^2+2b^2-c^2 \\[0.75em] B = a^2+c^2+2ac\cdot G \\[0.75em] %b^2 = a^2+c^2-2ac\cdot G \end{array}$

for $a,b,c$ (all other quantities [uppercase letters] are constants).

Does somebody has an idea?

Answer 1

Only by Resultant http://ipic.su/img/img7/fs/11.1558686948.png, where $C\to H$.