p+5=1-p(p-6)

Solution for p+5=1-p(p-6) equation:

p+5=1-p(p-6)

We move all terms to the left:

p+5-(1-p(p-6))=0


We calculate terms in parentheses: -(1-p(p-6)), so:

1-p(p-6)

determiningTheFunctionDomain
-p(p-6)+1

We multiply parentheses

-p^2+6p+1

We add all the numbers together, and all the variables

-1p^2+6p+1

Back to the equation:

-(-1p^2+6p+1)


We get rid of parentheses

1p^2-6p+p-1+5=0

We add all the numbers together, and all the variables

p^2-5p+4=0

a = 1; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·1·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*1}=\frac{2}{2}
=1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*1}=\frac{8}{2}
=4
$