8p^2-8p=12

Solution for 8p^2-8p=12 equation:

8p^2-8p=12

We move all terms to the left:

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

a = 8; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·8·(-12)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{7}}{2*8}=\frac{8-8\sqrt{7}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{7}}{2*8}=\frac{8+8\sqrt{7}}{16}
$