-4p(2p-8)=8-12p

Solution for -4p(2p-8)=8-12p equation:

-4p(2p-8)=8-12p

We move all terms to the left:

-4p(2p-8)-(8-12p)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-8p^2+32p-(-12p+8)=0

We get rid of parentheses

-8p^2+32p+12p-8=0

We add all the numbers together, and all the variables

-8p^2+44p-8=0

a = -8; b = 44; c = -8;
Δ = b2-4ac
Δ = 442-4·(-8)·(-8)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{105}}{2*-8}=\frac{-44-4\sqrt{105}}{-16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{105}}{2*-8}=\frac{-44+4\sqrt{105}}{-16}
$