(60-w)w=216

Solution for (60-w)w=216 equation:

(60-w)w=216

We move all terms to the left:

(60-w)w-(216)=0

We add all the numbers together, and all the variables

(-1w+60)w-216=0

We multiply parentheses

-1w^2+60w-216=0

a = -1; b = 60; c = -216;
Δ = b2-4ac
Δ = 602-4·(-1)·(-216)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{19}}{2*-1}=\frac{-60-12\sqrt{19}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{19}}{2*-1}=\frac{-60+12\sqrt{19}}{-2}
$