I'm reading this as X=(Xsqrt(2)/3)-(sqrt(3)/2).
X(1-sqrt(2)/3)=-sqrt(3)/2.
Square both sides:
X^2(1-2sqrt(2)/3+2/9)=3/4.
X^2(1-2.828/3+0.2222)=0.75.
0.2794X^2=0.75 so X^2=0.75/0.2794=2.6842.
X=±1.6384, but only one solution may be valid.
Try +1.6384 in original equation:
This value of X gives -sqrt(3) on right side, but X=-1.6384 does satisfy the original equation.
If my interpretation of the original problem is incorrect, I think you can still apply the method.