0=p(200-5p)

Solution for 0=p(200-5p) equation:

0=p(200-5p)

We move all terms to the left:

0-(p(200-5p))=0

We add all the numbers together, and all the variables

-(p(-5p+200))+0=0

We add all the numbers together, and all the variables

-(p(-5p+200))=0


We calculate terms in parentheses: -(p(-5p+200)), so:

p(-5p+200)

We multiply parentheses

-5p^2+200p

Back to the equation:

-(-5p^2+200p)


We get rid of parentheses

5p^2-200p=0

a = 5; b = -200; c = 0;
Δ = b2-4ac
Δ = -2002-4·5·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-200}{2*5}=\frac{0}{10}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+200}{2*5}=\frac{400}{10}
=40
$