(X-2)(3x-2)=8

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

(X-2)(3X-2)=8

We move all terms to the left:

(X-2)(3X-2)-(8)=0

We multiply parentheses ..

(+3X^2-2X-6X+4)-8=0

We get rid of parentheses

3X^2-2X-6X+4-8=0

We add all the numbers together, and all the variables

3X^2-8X-4=0

a = 3; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·3·(-4)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*3}=\frac{8-4\sqrt{7}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*3}=\frac{8+4\sqrt{7}}{6}
$