0.5=-0.1d^2+1.1d+0.5

Solution for 0.5=-0.1d^2+1.1d+0.5 equation:

0.5=-0.1d^2+1.1d+0.5

We move all terms to the left:

0.5-(-0.1d^2+1.1d+0.5)=0

We get rid of parentheses

0.1d^2-1.1d-0.5+0.5=0

We add all the numbers together, and all the variables

0.1d^2-1.1d=0

a = 0.1; b = -1.1; c = 0;
Δ = b2-4ac
Δ = -1.12-4·0.1·0
Δ = 1.21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.1)-\sqrt{1.21}}{2*0.1}=\frac{1.1-\sqrt{1.21}}{0.2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.1)+\sqrt{1.21}}{2*0.1}=\frac{1.1+\sqrt{1.21}}{0.2}
$