-12v-9v=4v^2

Solution for -12v-9v=4v^2 equation:

-12v-9v=4v^2

We move all terms to the left:

-12v-9v-(4v^2)=0

determiningTheFunctionDomain
-4v^2-12v-9v=0

We add all the numbers together, and all the variables

-4v^2-21v=0

a = -4; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-4)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-4}=\frac{0}{-8}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-4}=\frac{42}{-8}
=-5+1/4
$