8v^2+16v=-6

Solution for 8v^2+16v=-6 equation:

8v^2+16v=-6

We move all terms to the left:

8v^2+16v-(-6)=0

We add all the numbers together, and all the variables

8v^2+16v+6=0

a = 8; b = 16; c = +6;
Δ = b2-4ac
Δ = 162-4·8·6
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8}{2*8}=\frac{-24}{16}
=-1+1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8}{2*8}=\frac{-8}{16}
=-1/2
$