R=(2000+500n)(50-5n)

Solution for R=(2000+500n)(50-5n) equation:

=(2000+500R)(50-5R)

We move all terms to the left:

-((2000+500R)(50-5R))=0

We add all the numbers together, and all the variables

-((500R+2000)(-5R+50))=0

We multiply parentheses ..

-((-2500R^2+25000R-10000R+100000))=0


We calculate terms in parentheses: -((-2500R^2+25000R-10000R+100000)), so:

(-2500R^2+25000R-10000R+100000)

We get rid of parentheses

-2500R^2+25000R-10000R+100000

We add all the numbers together, and all the variables

-2500R^2+15000R+100000

Back to the equation:

-(-2500R^2+15000R+100000)


We get rid of parentheses

2500R^2-15000R-100000=0

a = 2500; b = -15000; c = -100000;
Δ = b2-4ac
Δ = -150002-4·2500·(-100000)
Δ = 1225000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225000000}=35000$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15000)-35000}{2*2500}=\frac{-20000}{5000}
=-4
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15000)+35000}{2*2500}=\frac{50000}{5000}
=10
$