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