3x(x+4)=12

Solution for 3x(x+4)=12 equation:

3x(x+4)=12

We move all terms to the left:

3x(x+4)-(12)=0

We multiply parentheses

3x^2+12x-12=0

a = 3; b = 12; c = -12;
Δ = b2-4ac
Δ = 122-4·3·(-12)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*3}=\frac{-12-12\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*3}=\frac{-12+12\sqrt{2}}{6}
$