(p-1)(p-1)=126

Solution for (p-1)(p-1)=126 equation:

(p-1)(p-1)=126

We move all terms to the left:

(p-1)(p-1)-(126)=0

We multiply parentheses ..

(+p^2-1p-1p+1)-126=0

We get rid of parentheses

p^2-1p-1p+1-126=0

We add all the numbers together, and all the variables

p^2-2p-125=0

a = 1; b = -2; c = -125;
Δ = b2-4ac
Δ = -22-4·1·(-125)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{14}}{2*1}=\frac{2-6\sqrt{14}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{14}}{2*1}=\frac{2+6\sqrt{14}}{2}
$