Answer
$\{1-\frac{1}{2}i,1+\frac{1}{2}i\}$
Work Step by Step
Step 1. Given the equation $4x^2=8x-5$, we have $4x^2-8x+4=4-5$ or $4(x-1)^2=-1$
Step 2. Solve the above equation to get $x-1=\pm\frac{1}{2}i$ or $x=1\pm\frac{1}{2}i$ or in set form as $\{1-\frac{1}{2}i,1+\frac{1}{2}i\}$
