-v^2+24v+16=6v^2

Solution for -v^2+24v+16=6v^2 equation:

-v^2+24v+16=6v^2

We move all terms to the left:

-v^2+24v+16-(6v^2)=0

determiningTheFunctionDomain
-v^2-6v^2+24v+16=0

We add all the numbers together, and all the variables

-7v^2+24v+16=0

a = -7; b = 24; c = +16;
Δ = b2-4ac
Δ = 242-4·(-7)·16
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-32}{2*-7}=\frac{-56}{-14}
=+4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+32}{2*-7}=\frac{8}{-14}
=-4/7
$