-8v+3v(v-6)=32

Solution for -8v+3v(v-6)=32 equation:

-8v+3v(v-6)=32

We move all terms to the left:

-8v+3v(v-6)-(32)=0

We multiply parentheses

3v^2-8v-18v-32=0

We add all the numbers together, and all the variables

3v^2-26v-32=0

a = 3; b = -26; c = -32;
Δ = b2-4ac
Δ = -262-4·3·(-32)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{265}}{2*3}=\frac{26-2\sqrt{265}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{265}}{2*3}=\frac{26+2\sqrt{265}}{6}
$