96+4d=d^2

Solution for 96+4d=d^2 equation:

96+4d=d^2

We move all terms to the left:

96+4d-(d^2)=0

determiningTheFunctionDomain
-d^2+4d+96=0

We add all the numbers together, and all the variables

-1d^2+4d+96=0

a = -1; b = 4; c = +96;
Δ = b2-4ac
Δ = 42-4·(-1)·96
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*-1}=\frac{-24}{-2}
=+12
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*-1}=\frac{16}{-2}
=-8
$