w(2w-30)-5400=0

Solution for w(2w-30)-5400=0 equation:

w(2w-30)-5400=0

We multiply parentheses

2w^2-30w-5400=0

a = 2; b = -30; c = -5400;
Δ = b2-4ac
Δ = -302-4·2·(-5400)
Δ = 44100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44100}=210$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-210}{2*2}=\frac{-180}{4}
=-45
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+210}{2*2}=\frac{240}{4}
=60
$