-3x(x+4)=6

Solution for -3x(x+4)=6 equation:

-3x(x+4)=6

We move all terms to the left:

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

We multiply parentheses

-3x^2-12x-6=0

a = -3; b = -12; c = -6;
Δ = b2-4ac
Δ = -122-4·(-3)·(-6)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{2}}{2*-3}=\frac{12-6\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{2}}{2*-3}=\frac{12+6\sqrt{2}}{-6}
$