1.
\(\displaystyle \text{if }\quad G=x- \frac{C}{x} \\\\\)
\(x
eq 0\)
Multiply both sides by x:
\(\displaystyle Gx=x\bigg(x- \frac{C}{x}\bigg )\\\\Gx=x^2-C\)
Subtract from both sides Gx:
\(Gx-Gx=x^2-C-Gx\\x^2-Gx-C=0\)
Then solve this equation:
\(\displaystyle x^2-Gx-C=0\\\\x_{1,2}= \frac{G\pm \sqrt{G^2+4C} }{2}\)
2.
\(\displaystyle\text{if}\quad G= \frac{x-C}{x}\)
\(x
eq 0\)
Multiply both sides by x:
\(Gx=x-C\)
Subtract from both sides Gx:
\(x-C-Gx=0\)
Then solve this equation:
\(\displaystyle x-Gx-C=0\\x(1-G)=C\\x= \frac{C}{1-G}\)
