2p^2-12p+12=-2

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

2p^2-12p+12=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

2p^2-12p+14=0

a = 2; b = -12; c = +14;
Δ = b2-4ac
Δ = -122-4·2·14
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{2}}{2*2}=\frac{12-4\sqrt{2}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{2}}{2*2}=\frac{12+4\sqrt{2}}{4}
$