#### Answer

$d=\pm \dfrac{9}{2}i$

#### Work Step by Step

Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $
4d^2+81=0
,$ are
\begin{array}{l}\require{cancel}
4d^2=-81
\\\\
d^2=\dfrac{-81}{4}
\\\\
d=\pm\sqrt{\dfrac{-81}{4}}
\\\\
d=\pm\sqrt{-1}\cdot\sqrt{\dfrac{81}{4}}
\\\\
d=\pm i\cdot\sqrt{\left( \dfrac{9}{2} \right)^2}
\\\\
d=\pm i\cdot\dfrac{9}{2}
\\\\
d=\pm \dfrac{9}{2}i
.\end{array}