2p^2-12p=22

Solution for 2p^2-12p=22 equation:

2p^2-12p=22

We move all terms to the left:

2p^2-12p-(22)=0

a = 2; b = -12; c = -22;
Δ = b2-4ac
Δ = -122-4·2·(-22)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{5}}{2*2}=\frac{12-8\sqrt{5}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{5}}{2*2}=\frac{12+8\sqrt{5}}{4}
$