8a2-4a=1

Solution for 8a2-4a=1 equation:

8a^2-4a=1

We move all terms to the left:

8a^2-4a-(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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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