(p+4)(p-6)=p-2p

Solution for (p+4)(p-6)=p-2p equation:

(p+4)(p-6)=p-2p

We move all terms to the left:

(p+4)(p-6)-(p-2p)=0

We add all the numbers together, and all the variables

(p+4)(p-6)-(-1p)=0

We get rid of parentheses

(p+4)(p-6)+1p=0

We multiply parentheses ..

(+p^2-6p+4p-24)+1p=0

We add all the numbers together, and all the variables

(+p^2-6p+4p-24)+p=0

We get rid of parentheses

p^2-6p+4p+p-24=0

We add all the numbers together, and all the variables

p^2-1p-24=0

a = 1; b = -1; c = -24;
Δ = b2-4ac
Δ = -12-4·1·(-24)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{97}}{2*1}=\frac{1-\sqrt{97}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*1}=\frac{1+\sqrt{97}}{2}
$