2p+p^2=7/9

Solution for 2p+p^2=7/9 equation:

2p+p^2=7/9

We move all terms to the left:

2p+p^2-(7/9)=0

We add all the numbers together, and all the variables

p^2+2p-(+7/9)=0

We get rid of parentheses

p^2+2p-7/9=0

We multiply all the terms by the denominator


p^2*9+2p*9-7=0

Wy multiply elements

9p^2+18p-7=0

a = 9; b = 18; c = -7;
Δ = b2-4ac
Δ = 182-4·9·(-7)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-24}{2*9}=\frac{-42}{18}
=-2+1/3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+24}{2*9}=\frac{6}{18}
=1/3
$