0=p(5000-25p)

Solution for 0=p(5000-25p) equation:

0=p(5000-25p)

We move all terms to the left:

0-(p(5000-25p))=0

We add all the numbers together, and all the variables

-(p(-25p+5000))+0=0

We add all the numbers together, and all the variables

-(p(-25p+5000))=0


We calculate terms in parentheses: -(p(-25p+5000)), so:

p(-25p+5000)

We multiply parentheses

-25p^2+5000p

Back to the equation:

-(-25p^2+5000p)


We get rid of parentheses

25p^2-5000p=0

a = 25; b = -5000; c = 0;
Δ = b2-4ac
Δ = -50002-4·25·0
Δ = 25000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25000000}=5000$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5000)-5000}{2*25}=\frac{0}{50}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5000)+5000}{2*25}=\frac{10000}{50}
=200
$