P(x)=((8x-x^2)/2)-10+x

Solution for P(x)=((8x-x^2)/2)-10+x equation:

(P)=((8P-P^2)/2)-10+P

We move all terms to the left:

(P)-(((8P-P^2)/2)-10+P)=0


Domain of the equation: 2)-10+P)!=0

P!=0/1

P!=0

P∈R


We multiply all the terms by the denominator


-(((8P-P^2)+P*2)-10+P)=0


We calculate terms in parentheses: -(((8P-P^2)+P*2)-10+P), so:

((8P-P^2)+P*2)-10+P

determiningTheFunctionDomain
((8P-P^2)+P*2)+P-10


We calculate terms in parentheses: +((8P-P^2)+P*2), so:

(8P-P^2)+P*2

Wy multiply elements

(8P-P^2)+2P

We get rid of parentheses

-P^2+8P+2P

We add all the numbers together, and all the variables

-1P^2+10P

Back to the equation:

+(-1P^2+10P)


We get rid of parentheses

-1P^2+10P+P-10

We add all the numbers together, and all the variables

-1P^2+11P-10

Back to the equation:

-(-1P^2+11P-10)


We get rid of parentheses

1P^2-11P+10=0

We add all the numbers together, and all the variables

P^2-11P+10=0

a = 1; b = -11; c = +10;
Δ = b2-4ac
Δ = -112-4·1·10
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{-(-11)-9}{2*1}=\frac{2}{2}
=1
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*1}=\frac{20}{2}
=10
$