2a(a+4)=12

Solution for 2a(a+4)=12 equation:

2a(a+4)=12

We move all terms to the left:

2a(a+4)-(12)=0

We multiply parentheses

2a^2+8a-12=0

a = 2; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·2·(-12)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*2}=\frac{-8-4\sqrt{10}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*2}=\frac{-8+4\sqrt{10}}{4}
$