2a(4a-1)=1

Solution for 2a(4a-1)=1 equation:

2a(4a-1)=1

We move all terms to the left:

2a(4a-1)-(1)=0

We multiply parentheses

8a^2-2a-1=0

a = 8; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·8·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*8}=\frac{-4}{16}
=-1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*8}=\frac{8}{16}
=1/2
$