2p^2-12p-1=31

Solution for 2p^2-12p-1=31 equation:

2p^2-12p-1=31

We move all terms to the left:

2p^2-12p-1-(31)=0

We add all the numbers together, and all the variables

2p^2-12p-32=0

a = 2; b = -12; c = -32;
Δ = b2-4ac
Δ = -122-4·2·(-32)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20}{2*2}=\frac{-8}{4}
=-2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*2}=\frac{32}{4}
=8
$