-3x(2x+6)=6

Solution for -3x(2x+6)=6 equation:

-3x(2x+6)=6

We move all terms to the left:

-3x(2x+6)-(6)=0

We multiply parentheses

-6x^2-18x-6=0

a = -6; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·(-6)·(-6)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{5}}{2*-6}=\frac{18-6\sqrt{5}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{5}}{2*-6}=\frac{18+6\sqrt{5}}{-12}
$