P(t)=P(t)(8-9P(t))

Solution for P(t)=P(t)(8-9P(t)) equation:

(P)=(P)(8-9(P))

We move all terms to the left:

(P)-((P)(8-9(P)))=0

We add all the numbers together, and all the variables

P-(P(-9P+8))=0


We calculate terms in parentheses: -(P(-9P+8)), so:

P(-9P+8)

We multiply parentheses

-9P^2+8P

Back to the equation:

-(-9P^2+8P)


We get rid of parentheses

9P^2-8P+P=0

We add all the numbers together, and all the variables

9P^2-7P=0

a = 9; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·9·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*9}=\frac{0}{18}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*9}=\frac{14}{18}
=7/9
$