6v^2+13v=8

Solution for 6v^2+13v=8 equation:

6v^2+13v=8

We move all terms to the left:

6v^2+13v-(8)=0

a = 6; b = 13; c = -8;
Δ = b2-4ac
Δ = 132-4·6·(-8)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-19}{2*6}=\frac{-32}{12}
=-2+2/3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+19}{2*6}=\frac{6}{12}
=1/2
$