v^2-12v-50=-6

Solution for v^2-12v-50=-6 equation:

v^2-12v-50=-6

We move all terms to the left:

v^2-12v-50-(-6)=0

We add all the numbers together, and all the variables

v^2-12v-44=0

a = 1; b = -12; c = -44;
Δ = b2-4ac
Δ = -122-4·1·(-44)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{5}}{2*1}=\frac{12-8\sqrt{5}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{5}}{2*1}=\frac{12+8\sqrt{5}}{2}
$