(30-w)w=216

Solution for (30-w)w=216 equation:

(30-w)w=216

We move all terms to the left:

(30-w)w-(216)=0

We add all the numbers together, and all the variables

(-1w+30)w-216=0

We multiply parentheses

-1w^2+30w-216=0

a = -1; b = 30; c = -216;
Δ = b2-4ac
Δ = 302-4·(-1)·(-216)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6}{2*-1}=\frac{-36}{-2}
=+18
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6}{2*-1}=\frac{-24}{-2}
=+12
$