Answer
$\displaystyle x=\frac{1}{2}\pm i$
Work Step by Step
$4x^{2}-4x+5=0$
We solve using the quadratic formula ($a=4,\ b=-4,\ c=5$):
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^{2}-4*4*5}}{2*4}$
$\displaystyle x=\frac{4\pm\sqrt{-64}}{8}$
$\displaystyle x=\frac{4\pm 8i}{8}$
$\displaystyle x=\frac{1}{2}\pm i$
