6.75=d^2

Solution for 6.75=d^2 equation:

6.75=d^2

We move all terms to the left:

6.75-(d^2)=0

We add all the numbers together, and all the variables

-1d^2+6.75=0

a = -1; b = 0; c = +6.75;
Δ = b2-4ac
Δ = 02-4·(-1)·6.75
Δ = 27
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:

$\sqrt{\Delta}=\sqrt{27}=\sqrt{9*3}=\sqrt{9}*\sqrt{3}=3\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{3}}{2*-1}=\frac{0-3\sqrt{3}}{-2}
=-\frac{3\sqrt{3}}{-2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{3}}{2*-1}=\frac{0+3\sqrt{3}}{-2}
=\frac{3\sqrt{3}}{-2}
$