0=0.5d^2+4d+4

Solution for 0=0.5d^2+4d+4 equation:

0=0.5d^2+4d+4

We move all terms to the left:

0-(0.5d^2+4d+4)=0

We add all the numbers together, and all the variables

-(0.5d^2+4d+4)=0

We get rid of parentheses

-0.5d^2-4d-4=0

a = -0.5; b = -4; c = -4;
Δ = b2-4ac
Δ = -42-4·(-0.5)·(-4)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{2}}{2*-0.5}=\frac{4-2\sqrt{2}}{-1}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{2}}{2*-0.5}=\frac{4+2\sqrt{2}}{-1}
$