3x(2x-6)=4

Solution for 3x(2x-6)=4 equation:

3x(2x-6)=4

We move all terms to the left:

3x(2x-6)-(4)=0

We multiply parentheses

6x^2-18x-4=0

a = 6; b = -18; c = -4;
Δ = b2-4ac
Δ = -182-4·6·(-4)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*6}=\frac{18-2\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*6}=\frac{18+2\sqrt{105}}{12}
$