2p-p^2=5/9

Solution for 2p-p^2=5/9 equation:

2p-p^2=5/9

We move all terms to the left:

2p-p^2-(5/9)=0

We add all the numbers together, and all the variables

-p^2+2p-(+5/9)=0

We add all the numbers together, and all the variables

-1p^2+2p-(+5/9)=0

We get rid of parentheses

-1p^2+2p-5/9=0

We multiply all the terms by the denominator


-1p^2*9+2p*9-5=0

Wy multiply elements

-9p^2+18p-5=0

a = -9; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·(-9)·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12}{2*-9}=\frac{-30}{-18}
=1+2/3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12}{2*-9}=\frac{-6}{-18}
=1/3
$