(p-1)(p-6)-126=0

Solution for (p-1)(p-6)-126=0 equation:

(p-1)(p-6)-126=0

We multiply parentheses ..

(+p^2-6p-1p+6)-126=0

We get rid of parentheses

p^2-6p-1p+6-126=0

We add all the numbers together, and all the variables

p^2-7p-120=0

a = 1; b = -7; c = -120;
Δ = b2-4ac
Δ = -72-4·1·(-120)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-23}{2*1}=\frac{-16}{2}
=-8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*1}=\frac{30}{2}
=15
$