12-8v^2=-2v^2-1

Solution for 12-8v^2=-2v^2-1 equation:

12-8v^2=-2v^2-1

We move all terms to the left:

12-8v^2-(-2v^2-1)=0

We get rid of parentheses

-8v^2+2v^2+1+12=0

We add all the numbers together, and all the variables

-6v^2+13=0

a = -6; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-6)·13
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{78}}{2*-6}=\frac{0-2\sqrt{78}}{-12}
=-\frac{2\sqrt{78}}{-12}
=-\frac{\sqrt{78}}{-6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{78}}{2*-6}=\frac{0+2\sqrt{78}}{-12}
=\frac{2\sqrt{78}}{-12}
=\frac{\sqrt{78}}{-6}
$