Solve 2x^n+10n=5

$$2 x ^ { n } + 10 n = 5$$

Solve for x (complex solution)

$$x=e^{\frac{Im(n)arg(\frac{5\left(1-2n\right)}{2})+iRe(n)arg(\frac{5\left(1-2n\right)}{2})}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}-\frac{2iRe(n)\pi n_{1}}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}-\frac{2\pi n_{1}Im(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}}\left(|\frac{5\left(1-2n\right)}{2}|\right)^{\frac{Re(n)-iIm(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$

Solve for x

$$\left\{\begin{matrix}x=\left(\frac{5}{2}-5n\right)^{\frac{1}{n}}\text{, }&\left(n\neq 0\text{ and }\left(\frac{5}{2}-5n\right)^{\frac{1}{n}}>0\text{ and }n<\frac{1}{2}\right)\text{ or }n=\frac{1}{2}\text{ or }\left(n\neq 0\text{ and }\left(\frac{5}{2}-5n\right)^{\frac{1}{n}}<0\text{ and }n<\frac{1}{2}\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(Numerator(n)\text{bmod}2=1\text{ and }Denominator(n)\text{bmod}2=1\text{ and }n>\frac{1}{2}\right)\\x=-\left(\frac{5}{2}-5n\right)^{\frac{1}{n}}\text{, }&\left(Numerator(n)\text{bmod}2=1\text{ and }Numerator(n)\text{bmod}2=0\text{ and }Denominator(n)\text{bmod}2=1\text{ and }n>\frac{1}{2}\right)\text{ or }\left(n<\frac{1}{2}\text{ and }n\neq 0\text{ and }\left(\frac{5}{2}-5n\right)^{\frac{1}{n}}>0\text{ and }Numerator(n)\text{bmod}2=0\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(n<\frac{1}{2}\text{ and }n\neq 0\text{ and }\left(\frac{5}{2}-5n\right)^{\frac{1}{n}}<0\text{ and }Numerator(n)\text{bmod}2=0\right)\end{matrix}\right.$$