(3d)^2=3^8

Solution for (3d)^2=3^8 equation:

(3d)^2=3^8

We move all terms to the left:

(3d)^2-(3^8)=0

We add all the numbers together, and all the variables

3d^2-6561=0

a = 3; b = 0; c = -6561;
Δ = b2-4ac
Δ = 02-4·3·(-6561)
Δ = 78732
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{78732}=\sqrt{26244*3}=\sqrt{26244}*\sqrt{3}=162\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-162\sqrt{3}}{2*3}=\frac{0-162\sqrt{3}}{6}
=-\frac{162\sqrt{3}}{6}
=-27\sqrt{3}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+162\sqrt{3}}{2*3}=\frac{0+162\sqrt{3}}{6}
=\frac{162\sqrt{3}}{6}
=27\sqrt{3}
$