(v+6)(v+6)=12

Solution for (v+6)(v+6)=12 equation:

(v+6)(v+6)=12

We move all terms to the left:

(v+6)(v+6)-(12)=0

We multiply parentheses ..

(+v^2+6v+6v+36)-12=0

We get rid of parentheses

v^2+6v+6v+36-12=0

We add all the numbers together, and all the variables

v^2+12v+24=0

a = 1; b = 12; c = +24;
Δ = b2-4ac
Δ = 122-4·1·24
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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