96=3v^2+12

Solution for 96=3v^2+12 equation:

96=3v^2+12

We move all terms to the left:

96-(3v^2+12)=0

We get rid of parentheses

-3v^2-12+96=0

We add all the numbers together, and all the variables

-3v^2+84=0

a = -3; b = 0; c = +84;
Δ = b2-4ac
Δ = 02-4·(-3)·84
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*-3}=\frac{0-12\sqrt{7}}{-6}
=-\frac{12\sqrt{7}}{-6}
=-\frac{2\sqrt{7}}{-1}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*-3}=\frac{0+12\sqrt{7}}{-6}
=\frac{12\sqrt{7}}{-6}
=\frac{2\sqrt{7}}{-1}
$