1500=-4d^2+200d-100

Solution for 1500=-4d^2+200d-100 equation:

1500=-4d^2+200d-100

We move all terms to the left:

1500-(-4d^2+200d-100)=0

We get rid of parentheses

4d^2-200d+100+1500=0

We add all the numbers together, and all the variables

4d^2-200d+1600=0

a = 4; b = -200; c = +1600;
Δ = b2-4ac
Δ = -2002-4·4·1600
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-120}{2*4}=\frac{80}{8}
=10
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+120}{2*4}=\frac{320}{8}
=40
$