2x(3x-6)=8

Solution for 2x(3x-6)=8 equation:

2x(3x-6)=8

We move all terms to the left:

2x(3x-6)-(8)=0

We multiply parentheses

6x^2-12x-8=0

a = 6; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·6·(-8)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{21}}{2*6}=\frac{12-4\sqrt{21}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{21}}{2*6}=\frac{12+4\sqrt{21}}{12}
$