2(w^2-21w+54)=0

Solution for 2(w^2-21w+54)=0 equation:

2(w^2-21w+54)=0

We multiply parentheses

2w^2-42w+108=0

a = 2; b = -42; c = +108;
Δ = b2-4ac
Δ = -422-4·2·108
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-30}{2*2}=\frac{12}{4}
=3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+30}{2*2}=\frac{72}{4}
=18
$