Question

Solve the following equations.
$3\cdot 2^{x/2}-7\cdot 2^{x/4}=20$

Answer 1

$2^{x/4}=t$

$3t^2-7t-20=0$

$3t^2-12t+5t-20=0$

$3t(t-4)+5(t-4)=0$

$t=4$ $t=-5/3$

$2^{x/4}=2^2$ $2^{x/4}=-5/3$

$\frac{x}{4}=2$ not possible

$x=8$