R(x)=1000(x)+.2(x)^2=

Solution for R(x)=1000(x)+.2(x)^2= equation:

(R)=1000(R)+.2(R)^2=

We move all terms to the left:

(R)-(1000(R)+.2(R)^2)=0

determiningTheFunctionDomain
-(1000R+.2R^2)+R=0

We get rid of parentheses

-.2R^2-1000R+R=0

We add all the numbers together, and all the variables

-0.2R^2-999R=0

a = -0.2; b = -999; c = 0;
Δ = b2-4ac
Δ = -9992-4·(-0.2)·0
Δ = 998001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{998001}=999$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-999)-999}{2*-0.2}=\frac{0}{-0.4}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-999)+999}{2*-0.2}=\frac{1998}{-0.4}
=-4995
$