Help needed

$$\boxed{2^{\frac{x}{2}} * 4^{\frac{x}{6}}* \left[(\frac{1}{8})^{\frac{1}{x}}\right]^{\frac{1}{6}}=2^2*2^{\frac{1}{3}} }\\\\ \Rightarrow 2^{\frac{x}{2}} *2^{2*\frac{x}{6}}*2^{-3*\frac{1}{x}*\frac{1}{6}}=2^{2+\frac{1}{3}}\\\\ \Rightarrow 2^{\frac{x}{2}} *2^{\frac{x}{3}}*2^{\left(-\frac{1}{2x}\right)}=2^{\frac{7}{3}}\\\\ \Rightarrow 2^{ \left(\frac{x}{2}+\frac{x}{3}-\frac{1}{2x}\right) }=2^{\frac{7}{3}} \quad | \quad ln\\\\ \Rightarrow { \left(\frac{x}{2}+\frac{x}{3}-\frac{1}{2x}\right)*\ln(2) }=\frac{7}{3}*\ln(2)\\\\ \Rightarrow { \frac{x}{2}+\frac{x}{3}-\frac{1}{2x}\right }=\frac{7}{3}\\\\$$

$$\\\Rightarrow { \frac{3x}{3x}*\frac{x}{2}+\frac{2x}{2x}*\frac{x}{3} -\frac{3}{3}*\frac{1}{2x}\right }=\frac{7}{3}\\\\ \Rightarrow \frac{3x^2+2x^2-3}{6x}=\frac{7}{3} \quad | \quad *6x\\\\ \Rightarrow 5x^2-3=6x*\frac{7}{3}\\ \Rightarrow 5x^2-3=14x\\$$

$$\\\Rightarrow 5x^2-14x-3=0\\\\ \Rightarrow x^2-\frac{14}{5}x-\frac{3}{5}=0\\\\ \Rightarrow x_{1,2}=\frac{14}{2*5}\pm\sqrt{\frac{14*14}{(2*5)*(2*5)}+\frac{3}{5}}\\\\ \Rightarrow x_{1,2}=\frac{14}{10}\pm\sqrt{\frac{14*14}{(10)*(10)}+\frac{20}{20}*\frac{3}{5}}\\\\ \Rightarrow x_{1,2}=\frac{14}{10}\pm\sqrt{\frac{196}{100}+\frac{60}{100}}\\\\ \Rightarrow x_{1,2}=\frac{14}{10}\pm\sqrt{\frac{196+60}{100}}\\\\ \Rightarrow x_{1,2}=\frac{14}{10}\pm\sqrt{\frac{256}{100}}\\\\ \Rightarrow x_{1,2}=\frac{14}{10}\pm\frac{16}{10}\\\\ \textcolor[rgb]{1,0,0}{x_1=}\frac{14}{10}+\frac{16}{10}=\frac{30}{10}=\textcolor[rgb]{1,0,0}{3}\\\\ \textcolor[rgb]{1,0,0}{x_2=}\frac{14}{10}-\frac{16}{10}=-\frac{2}{10}=\textcolor[rgb]{1,0,0}{-\frac{1}{5}}\\\\$$

Okay, so here's what happened.

I wrote a 2/3 page answer solving the thing, after which I checked my answers.

My answers were wrong 

Then I used an equation solver to check your equation and it gave me 

$$x_1=0.716$$

$$x_2=6.28$$

Did you by any chance miswrite something in your equation?

Currently you have this;

$$2^{2/x} * 4^{x/6}* ((1/8)^{1/x})^{1/6}=2^2*2^{1/3}$$

Oh sorry it was 2^(x/2), had to make an acount because i wasn't able do to the spamm security thing.