8v2-12v-14=0

Solution for 8v2-12v-14=0 equation:

8v^2-12v-14=0

a = 8; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·8·(-14)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{37}}{2*8}=\frac{12-4\sqrt{37}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{37}}{2*8}=\frac{12+4\sqrt{37}}{16}
$