2(d-4)2d=9

Solution for 2(d-4)2d=9 equation:

2(d-4)2d=9

We move all terms to the left:

2(d-4)2d-(9)=0

We multiply parentheses

4d^2-16d-9=0

a = 4; b = -16; c = -9;
Δ = b2-4ac
Δ = -162-4·4·(-9)
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{-(-16)-20}{2*4}=\frac{-4}{8}
=-1/2
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+20}{2*4}=\frac{36}{8}
=4+1/2
$