8(p-2)p=12

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

8(p-2)p=12

We move all terms to the left:

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

We multiply parentheses

8p^2-16p-12=0

a = 8; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·8·(-12)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{10}}{2*8}=\frac{16-8\sqrt{10}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{10}}{2*8}=\frac{16+8\sqrt{10}}{16}
$