8v^2=12

Solution for 8v^2=12 equation:

8v^2=12

We move all terms to the left:

8v^2-(12)=0

a = 8; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·8·(-12)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*8}=\frac{0-8\sqrt{6}}{16}
=-\frac{8\sqrt{6}}{16}
=-\frac{\sqrt{6}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*8}=\frac{0+8\sqrt{6}}{16}
=\frac{8\sqrt{6}}{16}
=\frac{\sqrt{6}}{2}
$