v2+16v+56=0=v=8

Solution for v2+16v+56=0=v=8 equation:

v2+16v+56=0=v=8

We add all the numbers together, and all the variables

v^2+16v+56=0

a = 1; b = 16; c = +56;
Δ = b2-4ac
Δ = 162-4·1·56
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{2}}{2*1}=\frac{-16-4\sqrt{2}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{2}}{2*1}=\frac{-16+4\sqrt{2}}{2}
$