6v^2=40-8v

Solution for 6v^2=40-8v equation:

6v^2=40-8v

We move all terms to the left:

6v^2-(40-8v)=0

We add all the numbers together, and all the variables

6v^2-(-8v+40)=0

We get rid of parentheses

6v^2+8v-40=0

a = 6; b = 8; c = -40;
Δ = b2-4ac
Δ = 82-4·6·(-40)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-32}{2*6}=\frac{-40}{12}
=-3+1/3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+32}{2*6}=\frac{24}{12}
=2
$