(30-w)w=108

Solution for (30-w)w=108 equation:

(30-w)w=108

We move all terms to the left:

(30-w)w-(108)=0

We add all the numbers together, and all the variables

(-1w+30)w-108=0

We multiply parentheses

-1w^2+30w-108=0

a = -1; b = 30; c = -108;
Δ = b2-4ac
Δ = 302-4·(-1)·(-108)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{13}}{2*-1}=\frac{-30-6\sqrt{13}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{13}}{2*-1}=\frac{-30+6\sqrt{13}}{-2}
$