6x(x+2)=12

Solution for 6x(x+2)=12 equation:

6x(x+2)=12

We move all terms to the left:

6x(x+2)-(12)=0

We multiply parentheses

6x^2+12x-12=0

a = 6; b = 12; c = -12;
Δ = b2-4ac
Δ = 122-4·6·(-12)
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{3}}{2*6}=\frac{-12-12\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{3}}{2*6}=\frac{-12+12\sqrt{3}}{12}
$