-3x(x+9)=-6

Solution for -3x(x+9)=-6 equation:

-3x(x+9)=-6

We move all terms to the left:

-3x(x+9)-(-6)=0

We add all the numbers together, and all the variables

-3x(x+9)+6=0

We multiply parentheses

-3x^2-27x+6=0

a = -3; b = -27; c = +6;
Δ = b2-4ac
Δ = -272-4·(-3)·6
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{89}}{2*-3}=\frac{27-3\sqrt{89}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{89}}{2*-3}=\frac{27+3\sqrt{89}}{-6}
$