P=(30+10n)(100-20n)

Solution for P=(30+10n)(100-20n) equation:

=(30+10P)(100-20P)

We move all terms to the left:

-((30+10P)(100-20P))=0

We add all the numbers together, and all the variables

-((10P+30)(-20P+100))=0

We multiply parentheses ..

-((-200P^2+1000P-600P+3000))=0


We calculate terms in parentheses: -((-200P^2+1000P-600P+3000)), so:

(-200P^2+1000P-600P+3000)

We get rid of parentheses

-200P^2+1000P-600P+3000

We add all the numbers together, and all the variables

-200P^2+400P+3000

Back to the equation:

-(-200P^2+400P+3000)


We get rid of parentheses

200P^2-400P-3000=0

a = 200; b = -400; c = -3000;
Δ = b2-4ac
Δ = -4002-4·200·(-3000)
Δ = 2560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2560000}=1600$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-1600}{2*200}=\frac{-1200}{400}
=-3
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+1600}{2*200}=\frac{2000}{400}
=5
$