3v^2+v=4

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

3v^2+v=4

We move all terms to the left:

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

a = 3; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·3·(-4)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*3}=\frac{-8}{6}
=-1+1/3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*3}=\frac{6}{6}
=1
$