challenging rational equation

${x \over x+1} + {3 \over x} = {5 \over 2x}$

${x \over x+1} + {6 \over 2x} = {5 \over 2x}$

${x \over x+1} = {5 \over 2x}- {6 \over 2x}$

${x \over x+1} = {-1 \over 2x}$

$2x^2 = -1(x+1)$

$2x^2 = -x - 1$

$2x^2 + x + 1 = 0$

$x = {-1 \pm \sqrt{(1)^2-4(2)(1)} \over 2(2)}$

$x = {-1 \pm \sqrt{-7} \over 4}$

$x = \color{brown}\boxed{{-1 \pm \sqrt{7}i \over 4}}$