96=6v^2/3

Solution for 96=6v^2/3 equation:

96=6v^2/3

We move all terms to the left:

96-(6v^2/3)=0

We get rid of parentheses

-6v^2/3+96=0

We multiply all the terms by the denominator


-6v^2+96*3=0

We add all the numbers together, and all the variables

-6v^2+288=0

a = -6; b = 0; c = +288;
Δ = b2-4ac
Δ = 02-4·(-6)·288
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{3}}{2*-6}=\frac{0-48\sqrt{3}}{-12}
=-\frac{48\sqrt{3}}{-12}
=-\frac{4\sqrt{3}}{-1}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*-6}=\frac{0+48\sqrt{3}}{-12}
=\frac{48\sqrt{3}}{-12}
=\frac{4\sqrt{3}}{-1}
$