1,500=-4d^2+200d-100

Solution for 1,500=-4d^2+200d-100 equation:

1.500=-4d^2+200d-100

We move all terms to the left:

1.500-(-4d^2+200d-100)=0

We add all the numbers together, and all the variables

-(-4d^2+200d-100)+1.5=0

We get rid of parentheses

4d^2-200d+100+1.5=0

We add all the numbers together, and all the variables

4d^2-200d+101.5=0

a = 4; b = -200; c = +101.5;
Δ = b2-4ac
Δ = -2002-4·4·101.5
Δ = 38376
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:

$\sqrt{\Delta}=\sqrt{38376}=\sqrt{36*1066}=\sqrt{36}*\sqrt{1066}=6\sqrt{1066}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-6\sqrt{1066}}{2*4}=\frac{200-6\sqrt{1066}}{8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+6\sqrt{1066}}{2*4}=\frac{200+6\sqrt{1066}}{8}
$