p+18=p(p-2)

Solution for p+18=p(p-2) equation:

p+18=p(p-2)

We move all terms to the left:

p+18-(p(p-2))=0


We calculate terms in parentheses: -(p(p-2)), so:

p(p-2)

We multiply parentheses

p^2-2p

Back to the equation:

-(p^2-2p)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1p^2+3p+18=0

a = -1; b = 3; c = +18;
Δ = b2-4ac
Δ = 32-4·(-1)·18
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-1}=\frac{-12}{-2}
=+6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-1}=\frac{6}{-2}
=-3
$