8v^2-16v-14=0

Solution for 8v^2-16v-14=0 equation:

8v^2-16v-14=0

a = 8; b = -16; c = -14;
Δ = b2-4ac
Δ = -162-4·8·(-14)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{11}}{2*8}=\frac{16-8\sqrt{11}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{11}}{2*8}=\frac{16+8\sqrt{11}}{16}
$