Solve ax^4a-5+5=3a

$$a x ^ { 4 a - 5 } + 5 = 3 a$$

Solve for x (complex solution)

$$x=e^{-\frac{8i\pi n_{1}Re(a)}{16\left(Re(a)\right)^{2}+16\left(Im(a)\right)^{2}-40Re(a)+25}-\frac{8\pi n_{1}Im(a)}{16\left(Re(a)\right)^{2}+16\left(Im(a)\right)^{2}-40Re(a)+25}+\frac{4arg(-\frac{5-3a}{a})Im(a)+4iRe(a)arg(-\frac{5-3a}{a})-5iarg(-\frac{5-3a}{a})}{16\left(Re(a)\right)^{2}+16\left(Im(a)\right)^{2}-40Re(a)+25}+\frac{10i\pi n_{1}}{16\left(Re(a)\right)^{2}+16\left(Im(a)\right)^{2}-40Re(a)+25}}\times \left(\frac{|5-3a|}{|a|}\right)^{\frac{-4iIm(a)+4Re(a)-5}{16\left(Re(a)\right)^{2}+16\left(Im(a)\right)^{2}-40Re(a)+25}}$$

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

$$a\neq 0$$

Solve for x

$$\left\{\begin{matrix}x=\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}\text{, }&\left(a\leq \frac{5}{3}\text{ and }Numerator(4a-5)\text{bmod}2=1\text{ and }a\neq \frac{5}{4}\text{ and }Denominator(4a)\text{bmod}2=1\text{ and }a>0\right)\text{ or }\left(\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}>0\text{ and }a>\frac{5}{3}\right)\text{ or }\left(\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}>0\text{ and }a<0\right)\text{ or }\left(\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}<0\text{ and }Denominator(4a)\text{bmod}2=1\text{ and }a>\frac{5}{3}\right)\text{ or }\left(\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}<0\text{ and }Denominator(4a)\text{bmod}2=1\text{ and }a<0\right)\\x=-\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}\text{, }&\left(Numerator(4a-5)\text{bmod}2=1\text{ and }a\neq \frac{5}{4}\text{ and }a>0\text{ and }Numerator(4a-5)\text{bmod}2=0\text{ and }Denominator(4a)\text{bmod}2=1\text{ and }a<\frac{5}{3}\right)\text{ or }\left(a<0\text{ and }\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}>0\text{ and }Numerator(4a-5)\text{bmod}2=0\text{ and }Denominator(4a)\text{bmod}2=1\right)\text{ or }\left(a>\frac{5}{3}\text{ and }\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}>0\text{ and }Numerator(4a-5)\text{bmod}2=0\text{ and }Denominator(4a)\text{bmod}2=1\right)\text{ or }\left(a>\frac{5}{3}\text{ and }\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}<0\text{ and }Numerator(4a-5)\text{bmod}2=0\right)\text{ or }\left(a<0\text{ and }\left(3-\frac{5}{a}\right)^{\frac{1}{4a-5}}<0\text{ and }Numerator(4a-5)\text{bmod}2=0\right)\end{matrix}\right.$$