9+6p=p^2-6p+20

Solution for 9+6p=p^2-6p+20 equation:

9+6p=p^2-6p+20

We move all terms to the left:

9+6p-(p^2-6p+20)=0

We get rid of parentheses

-p^2+6p+6p-20+9=0

We add all the numbers together, and all the variables

-1p^2+12p-11=0

a = -1; b = 12; c = -11;
Δ = b2-4ac
Δ = 122-4·(-1)·(-11)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-10}{2*-1}=\frac{-22}{-2}
=+11
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+10}{2*-1}=\frac{-2}{-2}
=1
$