(3g-6)(g-8)=42

Solution for (3g-6)(g-8)=42 equation:

(3g-6)(g-8)=42

We move all terms to the left:

(3g-6)(g-8)-(42)=0

We multiply parentheses ..

(+3g^2-24g-6g+48)-42=0

We get rid of parentheses

3g^2-24g-6g+48-42=0

We add all the numbers together, and all the variables

3g^2-30g+6=0

a = 3; b = -30; c = +6;
Δ = b2-4ac
Δ = -302-4·3·6
Δ = 828
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{23}}{2*3}=\frac{30-6\sqrt{23}}{6}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{23}}{2*3}=\frac{30+6\sqrt{23}}{6}
$