Answer
The equation has no solution.
Work Step by Step
$x^{\frac{3}{2}}+21=13$
$x^{\frac{3}{2}}=13-21$
$x^{\frac{3}{2}}=-8~~$ (Square both sides):
$(x^{\frac{3}{2}})^2=(-8)^2$
$x^3=64$
$x=\sqrt[3] {64}=4$
Check the solution:
$4^{\frac{3}{2}}+21=(\sqrt 4)^3+21=8+21=29\ne13$
