6v^2=4-8v

Solution for 6v^2=4-8v equation:

6v^2=4-8v

We move all terms to the left:

6v^2-(4-8v)=0

We add all the numbers together, and all the variables

6v^2-(-8v+4)=0

We get rid of parentheses

6v^2+8v-4=0

a = 6; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·6·(-4)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*6}=\frac{-8-4\sqrt{10}}{12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*6}=\frac{-8+4\sqrt{10}}{12}
$