V^2-3=16-9v^2

Solution for V^2-3=16-9v^2 equation:

^2-3=16-9V^2

We move all terms to the left:

^2-3-(16-9V^2)=0

We add all the numbers together, and all the variables

-(16-9V^2)=0

We get rid of parentheses

9V^2-16=0

a = 9; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·9·(-16)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*9}=\frac{-24}{18}
=-1+1/3
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*9}=\frac{24}{18}
=1+1/3
$