(X-6)(3x-1)=6

Solution for (X-6)(3x-1)=6 equation:

(X-6)(3X-1)=6

We move all terms to the left:

(X-6)(3X-1)-(6)=0

We multiply parentheses ..

(+3X^2-1X-18X+6)-6=0

We get rid of parentheses

3X^2-1X-18X+6-6=0

We add all the numbers together, and all the variables

3X^2-19X=0

a = 3; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·3·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*3}=\frac{38}{6}
=6+1/3
$