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

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Correct option is B

4x−3x−12=3x+12−22x−1⇒ 4x−3x3=3x3−4x2⇒ 32⋅4x=3x3+13⇒ 32⋅4x=3x⋅43⇒ 4x−141/2=3x−13⇒ 4x−3/2=3x−3/2⇒ 43x−3/2=1⇒ x−32=0⇒ x=3/2

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Number of solutions of equation 4x−3x−12=3x+12−22x−1 is

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