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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+48p^2+96p-8p-16)-12=0

We get rid of parentheses

48p^2+96p-8p-16-12=0

We add all the numbers together, and all the variables

48p^2+88p-28=0

a = 48; b = 88; c = -28;
Δ = b2-4ac
Δ = 882-4·48·(-28)
Δ = 13120
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:

$\sqrt{\Delta}=\sqrt{13120}=\sqrt{64*205}=\sqrt{64}*\sqrt{205}=8\sqrt{205}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-8\sqrt{205}}{2*48}=\frac{-88-8\sqrt{205}}{96}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+8\sqrt{205}}{2*48}=\frac{-88+8\sqrt{205}}{96}
$