Question

find the number such that the number exceeds its reciprocal by 3/2​

Answer 1

$x=\dfrac{1}{x}+\dfrac{3}{2}\Big |\cdot 2x\qquad(x\not=0)\\\\2x^2=2+3x\\2x^2-3x-2=0\\2x^2-4x+x-2=0\\2x(x-2)+1(x-2)=0\\(2x+1)(x-2)=0\\x=-\dfrac{1}{2} \vee x=2$