8a^2+12a+3=0

Solution for 8a^2+12a+3=0 equation:

8a^2+12a+3=0

a = 8; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·8·3
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{3}}{2*8}=\frac{-12-4\sqrt{3}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{3}}{2*8}=\frac{-12+4\sqrt{3}}{16}
$