(9+v)(3v-8)=0

Solution for (9+v)(3v-8)=0 equation:

(9+v)(3v-8)=0

We add all the numbers together, and all the variables

(v+9)(3v-8)=0

We multiply parentheses ..

(+3v^2-8v+27v-72)=0

We get rid of parentheses

3v^2-8v+27v-72=0

We add all the numbers together, and all the variables

3v^2+19v-72=0

a = 3; b = 19; c = -72;
Δ = b2-4ac
Δ = 192-4·3·(-72)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-35}{2*3}=\frac{-54}{6}
=-9
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+35}{2*3}=\frac{16}{6}
=2+2/3
$