0=-4d^2+200d-100

Solution for 0=-4d^2+200d-100 equation:

0=-4d^2+200d-100

We move all terms to the left:

0-(-4d^2+200d-100)=0

We add all the numbers together, and all the variables

-(-4d^2+200d-100)=0

We get rid of parentheses

4d^2-200d+100=0

a = 4; b = -200; c = +100;
Δ = b2-4ac
Δ = -2002-4·4·100
Δ = 38400
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:

$\sqrt{\Delta}=\sqrt{38400}=\sqrt{6400*6}=\sqrt{6400}*\sqrt{6}=80\sqrt{6}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-80\sqrt{6}}{2*4}=\frac{200-80\sqrt{6}}{8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+80\sqrt{6}}{2*4}=\frac{200+80\sqrt{6}}{8}
$