Solving Equations By Writing Them As Quadratics

Many equations not actually quadratic equations can be written as quadratics, solved as quadratics and these solution used to solve the original equation.
We can write the equation
$x-8 \sqrt{x}+12=0$
by substituting
$y= \sqrt{x}$
. 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
$\sqrt{x}=6 \rightarrow x=6^2=36$
.
$y=2$
then
$\sqrt{x}=2 \rightarrow x=2^2=4$
.