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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2-18x+2x-12)-6=0

We get rid of parentheses

3x^2-18x+2x-12-6=0

We add all the numbers together, and all the variables

3x^2-16x-18=0

a = 3; b = -16; c = -18;
Δ = b2-4ac
Δ = -162-4·3·(-18)
Δ = 472
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:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{118}}{2*3}=\frac{16-2\sqrt{118}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{118}}{2*3}=\frac{16+2\sqrt{118}}{6}
$