2a+4a^2=1

Solution for 2a+4a^2=1 equation:

2a+4a^2=1

We move all terms to the left:

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

a = 4; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·4·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*4}=\frac{-2-2\sqrt{5}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*4}=\frac{-2+2\sqrt{5}}{8}
$