Answer
$a =\frac{2±i\sqrt {6}}{2}$
Work Step by Step
$2a^2+5=4a$
$2a^2+5-4a=4a-4a$
$2a^2-4a+5=0$
$(2a^2-4a+5)/2=0/2$
$a^2-2a+5/2=0$
$a^2-2a+5/2+(-2/2)^2=0+(-2/2)^2$
$a^2-2a+5/2+(-1)^2=0+(-1)^2$
$a^2-2a+5/2+1=0+1$
$a^2-2a+5/2+1-5/2=0+1-5/2$
$a^2-2a+1=-3/2$
$(a-1)^2=-3/2$
$\sqrt {(a-1)^2} =\sqrt {-3/2}$
$(a-1) =\sqrt {-3*2/2*2}$
$(a-1) =\frac{\sqrt {-6}}{\sqrt 4}$
$(a-1) =\frac{\sqrt {-6}}{2}$
$(a-1) =\frac{±i\sqrt {6}}{2}$
$a-1+1 =1+\frac{±i\sqrt {6}}{2}$
$a-1+1 =\frac {2}{2}+\frac{±i\sqrt {6}}{2}$
$a =\frac{2±i\sqrt {6}}{2}$