(p^2-1)=39p

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

(p^2-1)=39p

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

p^2-39p-1=0

a = 1; b = -39; c = -1;
Δ = b2-4ac
Δ = -392-4·1·(-1)
Δ = 1525
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:

$\sqrt{\Delta}=\sqrt{1525}=\sqrt{25*61}=\sqrt{25}*\sqrt{61}=5\sqrt{61}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-5\sqrt{61}}{2*1}=\frac{39-5\sqrt{61}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+5\sqrt{61}}{2*1}=\frac{39+5\sqrt{61}}{2}
$