0=p^2-2p-11

Solution for 0=p^2-2p-11 equation:

0=p^2-2p-11

We move all terms to the left:

0-(p^2-2p-11)=0

We add all the numbers together, and all the variables

-(p^2-2p-11)=0

We get rid of parentheses

-p^2+2p+11=0

We add all the numbers together, and all the variables

-1p^2+2p+11=0

a = -1; b = 2; c = +11;
Δ = b2-4ac
Δ = 22-4·(-1)·11
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{3}}{2*-1}=\frac{-2-4\sqrt{3}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{3}}{2*-1}=\frac{-2+4\sqrt{3}}{-2}
$