8v(v+8)=12

Solution for 8v(v+8)=12 equation:

8v(v+8)=12

We move all terms to the left:

8v(v+8)-(12)=0

We multiply parentheses

8v^2+64v-12=0

a = 8; b = 64; c = -12;
Δ = b2-4ac
Δ = 642-4·8·(-12)
Δ = 4480
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:

$\sqrt{\Delta}=\sqrt{4480}=\sqrt{64*70}=\sqrt{64}*\sqrt{70}=8\sqrt{70}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{70}}{2*8}=\frac{-64-8\sqrt{70}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{70}}{2*8}=\frac{-64+8\sqrt{70}}{16}
$