8a^2-12a+1=0

Solution for 8a^2-12a+1=0 equation:

8a^2-12a+1=0

a = 8; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·8·1
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{7}}{2*8}=\frac{12-4\sqrt{7}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{7}}{2*8}=\frac{12+4\sqrt{7}}{16}
$