Number of solutions of equation $4^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}\text{ is }$

$\begin{array}{l}{4}^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}\\ \Rightarrow 4^x-\frac{3^x}{\sqrt{3}}=3^x\sqrt{3}-\frac{4^x}{2}\\ \Rightarrow \frac{3}{2}\cdot 4^x=3^x\left(\sqrt{3}+\frac{1}{\sqrt{3}}\right)\\ \Rightarrow \frac{3}{2}\cdot 4^x=3^x\cdot \frac{4}{\sqrt{3}}\\ \Rightarrow \frac{4^{x-1}}{4^{1/2}}=\frac{3^{x-1}}{\sqrt{3}}\\ \Rightarrow 4^{x-3/2}=3^{x-3/2}\\ \Rightarrow {\left(\frac{4}{3}\right)}^{x-3/2}=1\\ \Rightarrow x-\frac{3}{2}=0\\ \Rightarrow x=3/2\end{array}$