2v-3v2=-9

Solution for 2v-3v2=-9 equation:

2v-3v^2=-9

We move all terms to the left:

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

We add all the numbers together, and all the variables

-3v^2+2v+9=0

a = -3; b = 2; c = +9;
Δ = b2-4ac
Δ = 22-4·(-3)·9
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{7}}{2*-3}=\frac{-2-4\sqrt{7}}{-6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{7}}{2*-3}=\frac{-2+4\sqrt{7}}{-6}
$