R(x)=-2x^2-2000x

Solution for R(x)=-2x^2-2000x equation:

(R)=-2R^2-2000R

We move all terms to the left:

(R)-(-2R^2-2000R)=0

We get rid of parentheses

2R^2+2000R+R=0

We add all the numbers together, and all the variables

2R^2+2001R=0

a = 2; b = 2001; c = 0;
Δ = b2-4ac
Δ = 20012-4·2·0
Δ = 4004001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4004001}=2001$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2001)-2001}{2*2}=\frac{-4002}{4}
=-1000+1/2
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2001)+2001}{2*2}=\frac{0}{4}
=0
$