-97-16v=-6v^2

Solution for -97-16v=-6v^2 equation:

-97-16v=-6v^2

We move all terms to the left:

-97-16v-(-6v^2)=0

We get rid of parentheses

6v^2-16v-97=0

a = 6; b = -16; c = -97;
Δ = b2-4ac
Δ = -162-4·6·(-97)
Δ = 2584
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:

$\sqrt{\Delta}=\sqrt{2584}=\sqrt{4*646}=\sqrt{4}*\sqrt{646}=2\sqrt{646}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{646}}{2*6}=\frac{16-2\sqrt{646}}{12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{646}}{2*6}=\frac{16+2\sqrt{646}}{12}
$