p(1+p)=0.8

Solution for p(1+p)=0.8 equation:

p(1+p)=0.8

We move all terms to the left:

p(1+p)-(0.8)=0

We add all the numbers together, and all the variables

p(p+1)-(0.8)=0

We add all the numbers together, and all the variables

p(p+1)-0.8=0

We multiply parentheses

p^2+p-0.8=0

a = 1; b = 1; c = -0.8;
Δ = b2-4ac
Δ = 12-4·1·(-0.8)
Δ = 4.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{4.2}}{2*1}=\frac{-1-\sqrt{4.2}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{4.2}}{2*1}=\frac{-1+\sqrt{4.2}}{2}
$