-8p=4p^2-1

Solution for -8p=4p^2-1 equation:

-8p=4p^2-1

We move all terms to the left:

-8p-(4p^2-1)=0

We get rid of parentheses

-4p^2-8p+1=0

a = -4; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-4)·1
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{-(-8)-4\sqrt{5}}{2*-4}=\frac{8-4\sqrt{5}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{5}}{2*-4}=\frac{8+4\sqrt{5}}{-8}
$