(p^2-1)=39

Solution for (p^2-1)=39 equation:

(p^2-1)=39

We move all terms to the left:

(p^2-1)-(39)=0

We get rid of parentheses

p^2-1-39=0

We add all the numbers together, and all the variables

p^2-40=0

a = 1; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·1·(-40)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*1}=\frac{0-4\sqrt{10}}{2}
=-\frac{4\sqrt{10}}{2}
=-2\sqrt{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*1}=\frac{0+4\sqrt{10}}{2}
=\frac{4\sqrt{10}}{2}
=2\sqrt{10}
$