6v^2+8v=64

Solution for 6v^2+8v=64 equation:

6v^2+8v=64

We move all terms to the left:

6v^2+8v-(64)=0

a = 6; b = 8; c = -64;
Δ = b2-4ac
Δ = 82-4·6·(-64)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-40}{2*6}=\frac{-48}{12}
=-4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+40}{2*6}=\frac{32}{12}
=2+2/3
$