#### Answer

$x = ±\sqrt[3] \frac{9}{5}$ or $x=±\sqrt[3] {2}i$

#### Work Step by Step

$5x^6 + x^3 = 18$
Let $u=x^3$
Substitute.
$5u^2 + u = 18$
Get the factors.
$(5u-9)(u+2)=0$
$5u-9=0$ or $u+2=0$
$u=\frac{9}{5}$ or $u=-2$
Refer to the original substitution to get the value of $x$.
$u=x^3$
$\frac{9}{5}=x^3$ or $-2=x^3$
$x = ±\sqrt[3] \frac{9}{5}$ or $x=±\sqrt[3] {-2}$
$x = ±\sqrt[3] \frac{9}{5}$ or $x=±\sqrt[3] {2}i$