Many equations not actually quadratic equations can be written as quadratics, solved as quadratics and these solution used to solve the original equation. Some quintics - polynomials of degree four are especially suitable for this treatment.
We can write the equation
$x^4-8x^2+12=0$
by substituting
$y= x^2$
. The equation becomes
$y^2-8y+12=0$
.
This equation factorises as
$(y-6)(y-2)=0$
.
Set each factor equal to 0 and solve.
$y-6=0 \rightarrow y=6$

$y-2=0 \rightarrow y=2$

$y=6$
then
$x^2=6 \rightarrow x= \pm \sqrt{6}$
.
$y=2$
then
$x^2 =2 \rightarrow x= \pm \sqrt{2}$
.