(v-8)(3v+2)=v

Solution for (v-8)(3v+2)=v equation:

(v-8)(3v+2)=v

We move all terms to the left:

(v-8)(3v+2)-(v)=0

We add all the numbers together, and all the variables

-1v+(v-8)(3v+2)=0

We multiply parentheses ..

(+3v^2+2v-24v-16)-1v=0

We get rid of parentheses

3v^2+2v-24v-1v-16=0

We add all the numbers together, and all the variables

3v^2-23v-16=0

a = 3; b = -23; c = -16;
Δ = b2-4ac
Δ = -232-4·3·(-16)
Δ = 721
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{-(-23)-\sqrt{721}}{2*3}=\frac{23-\sqrt{721}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{721}}{2*3}=\frac{23+\sqrt{721}}{6}
$