P=n(70-n)

Solution for P=n(70-n) equation:

=P(70-P)

We move all terms to the left:

-(P(70-P))=0

We add all the numbers together, and all the variables

-(P(-1P+70))=0


We calculate terms in parentheses: -(P(-1P+70)), so:

P(-1P+70)

We multiply parentheses

-1P^2+70P

Back to the equation:

-(-1P^2+70P)


We get rid of parentheses

1P^2-70P=0

We add all the numbers together, and all the variables

P^2-70P=0

a = 1; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·1·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*1}=\frac{0}{2}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*1}=\frac{140}{2}
=70
$