(w-6)(w-6)(3)=42

Solution for (w-6)(w-6)(3)=42 equation:

(w-6)(w-6)(3)=42

We move all terms to the left:

(w-6)(w-6)(3)-(42)=0

We multiply parentheses ..

(+w^2-6w-6w+36)3-42=0

We multiply parentheses

3w^2-18w-18w+108-42=0

We add all the numbers together, and all the variables

3w^2-36w+66=0

a = 3; b = -36; c = +66;
Δ = b2-4ac
Δ = -362-4·3·66
Δ = 504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{14}}{2*3}=\frac{36-6\sqrt{14}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{14}}{2*3}=\frac{36+6\sqrt{14}}{6}
$