12v^2-8v+3=6v

Solution for 12v^2-8v+3=6v equation:

12v^2-8v+3=6v

We move all terms to the left:

12v^2-8v+3-(6v)=0

We add all the numbers together, and all the variables

12v^2-14v+3=0

a = 12; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·12·3
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{13}}{2*12}=\frac{14-2\sqrt{13}}{24}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{13}}{2*12}=\frac{14+2\sqrt{13}}{24}
$