Answer
$x=5\ in$ and $x=12.2\ in$
Work Step by Step
Step 1. Use the given formula
$V=x(x+10)(30-2x)=x(30x-2x^2+300-20x)=-2x^3+10x^2+300x$
and letting $V=1500$, we have
$x^3-5x^2-150x+750=0$
Step 2. Using synthetic division, we can find a zero at $x=5$, as shown in the figure, and the above equation becomes
$(x-5)(x^2-150)=0$
Step 3. As $x\geq0$, the second solution can be found as
$x=\sqrt {150}\approx12.2\ in$
Step 4. We conclude the two possible solutions are $x=5\ in$ and $x=12.2\ in$
