V(x)=4x-39x^2+93.5x

Solution for V(x)=4x-39x^2+93.5x equation:

(V)=4V-39V^2+93.5V

We move all terms to the left:

(V)-(4V-39V^2+93.5V)=0

We get rid of parentheses

39V^2-4V-93.5V+V=0

We add all the numbers together, and all the variables

39V^2-96.5V=0

a = 39; b = -96.5; c = 0;
Δ = b2-4ac
Δ = -96.52-4·39·0
Δ = 9312.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96.5)-\sqrt{9312.25}}{2*39}=\frac{96.5-\sqrt{9312.25}}{78}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96.5)+\sqrt{9312.25}}{2*39}=\frac{96.5+\sqrt{9312.25}}{78}
$