-2(p-3)(p-9)=0

Solution for -2(p-3)(p-9)=0 equation:

-2(p-3)(p-9)=0

We multiply parentheses ..

-2(+p^2-9p-3p+27)=0

We multiply parentheses

-2p^2+18p+6p-54=0

We add all the numbers together, and all the variables

-2p^2+24p-54=0

a = -2; b = 24; c = -54;
Δ = b2-4ac
Δ = 242-4·(-2)·(-54)
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{-(24)-12}{2*-2}=\frac{-36}{-4}
=+9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*-2}=\frac{-12}{-4}
=+3
$