6(3a+6)(4a-2)=4

Solution for 6(3a+6)(4a-2)=4 equation:

6(3a+6)(4a-2)=4

We move all terms to the left:

6(3a+6)(4a-2)-(4)=0

We multiply parentheses ..

6(+12a^2-6a+24a-12)-4=0

We multiply parentheses

72a^2-36a+144a-72-4=0

We add all the numbers together, and all the variables

72a^2+108a-76=0

a = 72; b = 108; c = -76;
Δ = b2-4ac
Δ = 1082-4·72·(-76)
Δ = 33552
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:

$\sqrt{\Delta}=\sqrt{33552}=\sqrt{144*233}=\sqrt{144}*\sqrt{233}=12\sqrt{233}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-12\sqrt{233}}{2*72}=\frac{-108-12\sqrt{233}}{144}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+12\sqrt{233}}{2*72}=\frac{-108+12\sqrt{233}}{144}
$