8v^2-16v-86=-10

Solution for 8v^2-16v-86=-10 equation:

8v^2-16v-86=-10

We move all terms to the left:

8v^2-16v-86-(-10)=0

We add all the numbers together, and all the variables

8v^2-16v-76=0

a = 8; b = -16; c = -76;
Δ = b2-4ac
Δ = -162-4·8·(-76)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{42}}{2*8}=\frac{16-8\sqrt{42}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{42}}{2*8}=\frac{16+8\sqrt{42}}{16}
$