4v^2+3=-9v

Solution for 4v^2+3=-9v equation:

4v^2+3=-9v

We move all terms to the left:

4v^2+3-(-9v)=0

We get rid of parentheses

4v^2+9v+3=0

a = 4; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·4·3
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{33}}{2*4}=\frac{-9-\sqrt{33}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{33}}{2*4}=\frac{-9+\sqrt{33}}{8}
$