8v^2-16v-7=0

Solution for 8v^2-16v-7=0 equation:

8v^2-16v-7=0

a = 8; b = -16; c = -7;
Δ = b2-4ac
Δ = -162-4·8·(-7)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{30}}{2*8}=\frac{16-4\sqrt{30}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{30}}{2*8}=\frac{16+4\sqrt{30}}{16}
$