Solve for x.

After you find a possible solution, it would be a good idea to plug the possible solution into the origional equation to see if the possible solution is a solution which I will do now.

$\frac{{2(0.406228)}^{2}}{\sqrt{{0.406228}^{4}}}+2=\frac{5}{\sqrt{{3}^{0.406228}}}$

$\frac{2(0.165021187984)}{\sqrt{{0.406228}^{4}}}+2=\frac{5}{\sqrt{{3}^{0.406228}}}$

$\frac{0.330042375968}{\sqrt{{0.406228}^{4}}}+2=\frac{5}{\sqrt{{3}^{0.406228}}}$

$\frac{0.330042375968}{\sqrt{0.0272319924836507}}+2=\frac{5}{\sqrt{{3}^{0.406228}}}$

$\frac{0.330042375968}{0.1650211879840001031}+2=\frac{5}{\sqrt{{3}^{0.406228}}}$

$1.9999999999999987504635 +2=\frac{5}{\sqrt{{3}^{0.406228}}}$

$3.9999999999999987504635 =\frac{5}{\sqrt{{3}^{0.406228}}}$

$3.9999999999999987504635 =\frac{5}{\sqrt{1.5624999533947653}}$

$3.9999999999999987504635 =\frac{5}{1.249999981357905981}$

$3.9999999999999987504635 = 4.000000059654701750471$

$3.9999999999999987504635 ≠ 4.000000059654701750471$

Because only one possible solution was found and it turned out not to be a solution, there is no solution.