3v^2+36v+4=8v

Solution for 3v^2+36v+4=8v equation:

3v^2+36v+4=8v

We move all terms to the left:

3v^2+36v+4-(8v)=0

We add all the numbers together, and all the variables

3v^2+28v+4=0

a = 3; b = 28; c = +4;
Δ = b2-4ac
Δ = 282-4·3·4
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{46}}{2*3}=\frac{-28-4\sqrt{46}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{46}}{2*3}=\frac{-28+4\sqrt{46}}{6}
$