-8v^2-2v+12=9

Solution for -8v^2-2v+12=9 equation:

-8v^2-2v+12=9

We move all terms to the left:

-8v^2-2v+12-(9)=0

We add all the numbers together, and all the variables

-8v^2-2v+3=0

a = -8; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-8)·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-8}=\frac{-8}{-16}
=1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-8}=\frac{12}{-16}
=-3/4
$