#### Answer

The solution is $x=\sqrt[5]{4}$

#### Work Step by Step

$6x^{5/2}-12=0$
Take $12$ to the right side:
$6x^{5/2}=12$
Take the $6$ to divide the right side:
$x^{5/2}=\dfrac{12}{6}$
$x^{5/2}=2$
Raise both sides to $\dfrac{2}{5}$:
$(x^{5/2})^{2/5}=2^{2/5}$
$x=\sqrt[5]{2^{2}}$
$x=\sqrt[5]{4}$