P=(90+5x)(200-10x)

Solution for P=(90+5x)(200-10x) equation:

=(90+5P)(200-10P)

We move all terms to the left:

-((90+5P)(200-10P))=0

We add all the numbers together, and all the variables

-((5P+90)(-10P+200))=0

We multiply parentheses ..

-((-50P^2+1000P-900P+18000))=0


We calculate terms in parentheses: -((-50P^2+1000P-900P+18000)), so:

(-50P^2+1000P-900P+18000)

We get rid of parentheses

-50P^2+1000P-900P+18000

We add all the numbers together, and all the variables

-50P^2+100P+18000

Back to the equation:

-(-50P^2+100P+18000)


We get rid of parentheses

50P^2-100P-18000=0

a = 50; b = -100; c = -18000;
Δ = b2-4ac
Δ = -1002-4·50·(-18000)
Δ = 3610000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3610000}=1900$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-1900}{2*50}=\frac{-1800}{100}
=-18
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+1900}{2*50}=\frac{2000}{100}
=20
$