12v2+v=6

Solution for 12v2+v=6 equation:

12v^2+v=6

We move all terms to the left:

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

a = 12; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·12·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*12}=\frac{-18}{24}
=-3/4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*12}=\frac{16}{24}
=2/3
$