V=36a(9-7)-24(7)(2(9)-3(7))+2(9)(-2(3(9)+(7)))

Solution for V=36a(9-7)-24(7)(2(9)-3(7))+2(9)(-2(3(9)+(7))) equation:

=36V(9-7)-24(7)(2(9)-3(7))+2(9)(-2(3(9)+(7)))

We move all terms to the left:

-(36V(9-7)-24(7)(2(9)-3(7))+2(9)(-2(3(9)+(7))))=0

We add all the numbers together, and all the variables

-(36V2-247(-8)+29(-246))=0


We calculate terms in parentheses: -(36V2-247(-8)+29(-246)), so:

36V2-247(-8)+29(-246)

We add all the numbers together, and all the variables

36V^2-5158

Back to the equation:

-(36V^2-5158)


We get rid of parentheses

-36V^2+5158=0

a = -36; b = 0; c = +5158;
Δ = b2-4ac
Δ = 02-4·(-36)·5158
Δ = 742752
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{742752}=\sqrt{144*5158}=\sqrt{144}*\sqrt{5158}=12\sqrt{5158}$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5158}}{2*-36}=\frac{0-12\sqrt{5158}}{-72}
=-\frac{12\sqrt{5158}}{-72}
=-\frac{\sqrt{5158}}{-6}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5158}}{2*-36}=\frac{0+12\sqrt{5158}}{-72}
=\frac{12\sqrt{5158}}{-72}
=\frac{\sqrt{5158}}{-6}
$