-4(4+7p)-3p(-8-2p)=p

Solution for -4(4+7p)-3p(-8-2p)=p equation:

-4(4+7p)-3p(-8-2p)=p

We move all terms to the left:

-4(4+7p)-3p(-8-2p)-(p)=0

We add all the numbers together, and all the variables

-4(7p+4)-3p(-2p-8)-p=0

We add all the numbers together, and all the variables

-1p-4(7p+4)-3p(-2p-8)=0

We multiply parentheses

6p^2-1p-28p+24p-16=0

We add all the numbers together, and all the variables

6p^2-5p-16=0

a = 6; b = -5; c = -16;
Δ = b2-4ac
Δ = -52-4·6·(-16)
Δ = 409
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{-(-5)-\sqrt{409}}{2*6}=\frac{5-\sqrt{409}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{409}}{2*6}=\frac{5+\sqrt{409}}{12}
$