3v^2=-6v+8

Solution for 3v^2=-6v+8 equation:

3v^2=-6v+8

We move all terms to the left:

3v^2-(-6v+8)=0

We get rid of parentheses

3v^2+6v-8=0

a = 3; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·3·(-8)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*3}=\frac{-6-2\sqrt{33}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*3}=\frac{-6+2\sqrt{33}}{6}
$