p-5(p+4)p=(8-p)

Solution for p-5(p+4)p=(8-p) equation:

p-5(p+4)p=(8-p)

We move all terms to the left:

p-5(p+4)p-((8-p))=0

We add all the numbers together, and all the variables

p-5(p+4)p-((-1p+8))=0

We multiply parentheses

-5p^2+p-20p-((-1p+8))=0


We calculate terms in parentheses: -((-1p+8)), so:

(-1p+8)

We get rid of parentheses

-1p+8

Back to the equation:

-(-1p+8)


We add all the numbers together, and all the variables

-5p^2-19p-(-1p+8)=0

We get rid of parentheses

-5p^2-19p+1p-8=0

We add all the numbers together, and all the variables

-5p^2-18p-8=0

a = -5; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·(-5)·(-8)
Δ = 164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{41}}{2*-5}=\frac{18-2\sqrt{41}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{41}}{2*-5}=\frac{18+2\sqrt{41}}{-10}
$