Επίλυση 2/5nx-n^2/x+x/10=7/15-frac{x}{3}+frac{nx}{2}

$$\frac { 2 } { 5 } n x - \frac { n ^ { 2 } } { x } + \frac { x } { 10 } = \frac { 7 } { 15 } - \frac { x } { 3 } + \frac { n x } { 2 }$$

Λύση ως προς n (complex solution)

$$n=-\frac{\sqrt{9x^{4}+1560x^{2}-1680x}}{60}-\frac{x^{2}}{20}$$

$$n=\frac{\sqrt{9x^{4}+1560x^{2}-1680x}}{60}-\frac{x^{2}}{20}\text{, }x\neq 0$$

Λύση ως προς x (complex solution)

$$\left\{\begin{matrix}x=\frac{-\sqrt{49+390n^{2}-90n^{3}}+7}{13-3n}\text{, }&n\neq 0\text{ and }n\neq \frac{13}{3}\\x=\frac{\sqrt{49+390n^{2}-90n^{3}}+7}{13-3n}\text{, }&n\neq \frac{13}{3}\\x=-\frac{845}{21}\text{, }&n=\frac{13}{3}\end{matrix}\right,$$

Λύση ως προς n

$$n=-\frac{\sqrt{9x^{4}+1560x^{2}-1680x}}{60}-\frac{x^{2}}{20}$$

$$n=\frac{\sqrt{9x^{4}+1560x^{2}-1680x}}{60}-\frac{x^{2}}{20}\text{, }9x^{4}+1560x^{2}-1680x\geq 0\text{ and }x\neq 0$$

Λύση ως προς x

$$\left\{\begin{matrix}x=\frac{-\sqrt{49+390n^{2}-90n^{3}}+7}{13-3n}\text{, }&n\neq 0\text{ and }n\neq \frac{13}{3}\text{ and }30\left(13-3n\right)n^{2}\geq -49\text{ and }49+390n^{2}-90n^{3}\geq 0\\x=\frac{\sqrt{49+390n^{2}-90n^{3}}+7}{13-3n}\text{, }&n\neq \frac{13}{3}\text{ and }390n^{2}-90n^{3}\geq -49\text{ and }49+390n^{2}-90n^{3}\geq 0\\x=-\frac{845}{21}\text{, }&n=\frac{13}{3}\end{matrix}\right,$$