2v^2-32=-12v

Solution for 2v^2-32=-12v equation:

2v^2-32=-12v

We move all terms to the left:

2v^2-32-(-12v)=0

We get rid of parentheses

2v^2+12v-32=0

a = 2; b = 12; c = -32;
Δ = b2-4ac
Δ = 122-4·2·(-32)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20}{2*2}=\frac{-32}{4}
=-8
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20}{2*2}=\frac{8}{4}
=2
$