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

Solution for (4a+2)(2a-1)+1=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8a^2-1=0

a = 8; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·8·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*8}=\frac{0-4\sqrt{2}}{16}
=-\frac{4\sqrt{2}}{16}
=-\frac{\sqrt{2}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*8}=\frac{0+4\sqrt{2}}{16}
=\frac{4\sqrt{2}}{16}
=\frac{\sqrt{2}}{4}
$