27-4d=d^2

Solution for 27-4d=d^2 equation:

27-4d=d^2

We move all terms to the left:

27-4d-(d^2)=0

determiningTheFunctionDomain
-d^2-4d+27=0

We add all the numbers together, and all the variables

-1d^2-4d+27=0

a = -1; b = -4; c = +27;
Δ = b2-4ac
Δ = -42-4·(-1)·27
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{31}}{2*-1}=\frac{4-2\sqrt{31}}{-2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{31}}{2*-1}=\frac{4+2\sqrt{31}}{-2}
$