Risolvi k_{c}=x^2/(10-x)(20-x)

$$k _ { c } = \frac { x ^ { 2 } } { ( 10 - x ) ( 20 - x ) }$$

Trova x (soluzione complessa)

$$\left\{\begin{matrix}x=\frac{5\left(\sqrt{k_{c}\left(k_{c}+8\right)}+3k_{c}\right)}{k_{c}-1}\text{; }x=\frac{5\left(-\sqrt{k_{c}\left(k_{c}+8\right)}+3k_{c}\right)}{k_{c}-1}\text{, }&k_{c}\neq 1\\x=\frac{20}{3}\text{, }&k_{c}=1\end{matrix}\right,$$

Trova k_c

$$k_{c}=\frac{x^{2}}{\left(x-20\right)\left(x-10\right)}$$

$$x\neq 10\text{ and }x\neq 20$$

Trova x

$$\left\{\begin{matrix}x=\frac{5\left(\sqrt{k_{c}\left(k_{c}+8\right)}+3k_{c}\right)}{k_{c}-1}\text{; }x=\frac{5\left(-\sqrt{k_{c}\left(k_{c}+8\right)}+3k_{c}\right)}{k_{c}-1}\text{, }&\left(k_{c}\neq 1\text{ and }k_{c}\geq 0\right)\text{ or }k_{c}\leq -8\\x=\frac{20}{3}\text{, }&k_{c}=1\end{matrix}\right,$$