p^2-5=15

Solution for p^2-5=15 equation:

p^2-5=15

We move all terms to the left:

p^2-5-(15)=0

We add all the numbers together, and all the variables

p^2-20=0

a = 1; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·1·(-20)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*1}=\frac{0-4\sqrt{5}}{2}
=-\frac{4\sqrt{5}}{2}
=-2\sqrt{5}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*1}=\frac{0+4\sqrt{5}}{2}
=\frac{4\sqrt{5}}{2}
=2\sqrt{5}
$