3a(4a-8)=-2

Solution for 3a(4a-8)=-2 equation:

3a(4a-8)=-2

We move all terms to the left:

3a(4a-8)-(-2)=0

We add all the numbers together, and all the variables

3a(4a-8)+2=0

We multiply parentheses

12a^2-24a+2=0

a = 12; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·12·2
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{30}}{2*12}=\frac{24-4\sqrt{30}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{30}}{2*12}=\frac{24+4\sqrt{30}}{24}
$