3(a+4);a=6

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

3(a+4)a=6

We move all terms to the left:

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

We multiply parentheses

3a^2+12a-6=0

a = 3; b = 12; c = -6;
Δ = b2-4ac
Δ = 122-4·3·(-6)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{6}}{2*3}=\frac{-12-6\sqrt{6}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{6}}{2*3}=\frac{-12+6\sqrt{6}}{6}
$