6v^2-12v-71=-2

Solution for 6v^2-12v-71=-2 equation:

6v^2-12v-71=-2

We move all terms to the left:

6v^2-12v-71-(-2)=0

We add all the numbers together, and all the variables

6v^2-12v-69=0

a = 6; b = -12; c = -69;
Δ = b2-4ac
Δ = -122-4·6·(-69)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-30\sqrt{2}}{2*6}=\frac{12-30\sqrt{2}}{12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+30\sqrt{2}}{2*6}=\frac{12+30\sqrt{2}}{12}
$