8p-4p(p-4)=-12-(p-8)

Solution for 8p-4p(p-4)=-12-(p-8) equation:

8p-4p(p-4)=-12-(p-8)

We move all terms to the left:

8p-4p(p-4)-(-12-(p-8))=0

We multiply parentheses

-4p^2+8p+16p-(-12-(p-8))=0


We calculate terms in parentheses: -(-12-(p-8)), so:

-12-(p-8)

determiningTheFunctionDomain
-(p-8)-12

We get rid of parentheses

-p+8-12

We add all the numbers together, and all the variables

-1p-4

Back to the equation:

-(-1p-4)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-4p^2+24p+1p+4=0

We add all the numbers together, and all the variables

-4p^2+25p+4=0

a = -4; b = 25; c = +4;
Δ = b2-4ac
Δ = 252-4·(-4)·4
Δ = 689
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{-(25)-\sqrt{689}}{2*-4}=\frac{-25-\sqrt{689}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{689}}{2*-4}=\frac{-25+\sqrt{689}}{-8}
$