8p^2+4p=1

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

8p^2+4p=1

We move all terms to the left:

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

a = 8; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·8·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{3}}{2*8}=\frac{-4-4\sqrt{3}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{3}}{2*8}=\frac{-4+4\sqrt{3}}{16}
$