V=72w-4w^2

Solution for V=72w-4w^2 equation:

=72V-4V^2

We move all terms to the left:

-(72V-4V^2)=0

We get rid of parentheses

4V^2-72V=0

a = 4; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·4·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*4}=\frac{0}{8}
=0
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*4}=\frac{144}{8}
=18
$