4a-12a^2+1=0

Solution for 4a-12a^2+1=0 equation:

4a-12a^2+1=0

a = -12; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-12)·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*-12}=\frac{-12}{-24}
=1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-12}=\frac{4}{-24}
=-1/6
$