Answer
$x=3±\frac{i\sqrt{5}}{2} $
Work Step by Step
$4x^2-24x+41=0$
$(4x^2-24x+41)/4=0/4$
$x^2-6x+41/4=0$
$x^2-6x+41/4+(-6/2)^2=0+(-6/2)^2$
$x^2-6x+41/4+(-3)^2=0+(-3)^2$
$x^2-6x+41/4+9=9$
$x^2-6x+41/4+9-41/4=9-41/4$
$x^2-6x+9=-5/4$
$(x-3)^2=-5/4$
$\sqrt{(x-3)^2}=\sqrt{-5/4}$
$(x-3)=\sqrt{-5/4}$
$(x-3)=\sqrt{-5}/2$
$x-3+3=\sqrt{-5}/2 +3$
$x=3±\sqrt{-5}/2 $
$x=3±\frac{i\sqrt{5}}{2} $
