X(3x-3)=6

Solution for X(3x-3)=6 equation:

X(3X-3)=6

We move all terms to the left:

X(3X-3)-(6)=0

We multiply parentheses

3X^2-3X-6=0

a = 3; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·3·(-6)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*3}=\frac{-6}{6}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*3}=\frac{12}{6}
=2
$