-200v=-16v^2-96

Solution for -200v=-16v^2-96 equation:

-200v=-16v^2-96

We move all terms to the left:

-200v-(-16v^2-96)=0

We get rid of parentheses

16v^2-200v+96=0

a = 16; b = -200; c = +96;
Δ = b2-4ac
Δ = -2002-4·16·96
Δ = 33856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33856}=184$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-184}{2*16}=\frac{16}{32}
=1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+184}{2*16}=\frac{384}{32}
=12
$