V=(40-x)(60-x)

Solution for V=(40-x)(60-x) equation:

=(40-V)(60-V)

We move all terms to the left:

-((40-V)(60-V))=0

We add all the numbers together, and all the variables

-((-1V+40)(-1V+60))=0

We multiply parentheses ..

-((+V^2-60V-40V+2400))=0


We calculate terms in parentheses: -((+V^2-60V-40V+2400)), so:

(+V^2-60V-40V+2400)

We get rid of parentheses

V^2-60V-40V+2400

We add all the numbers together, and all the variables

V^2-100V+2400

Back to the equation:

-(V^2-100V+2400)


We get rid of parentheses

-V^2+100V-2400=0

We add all the numbers together, and all the variables

-1V^2+100V-2400=0

a = -1; b = 100; c = -2400;
Δ = b2-4ac
Δ = 1002-4·(-1)·(-2400)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20}{2*-1}=\frac{-120}{-2}
=+60
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20}{2*-1}=\frac{-80}{-2}
=+40
$