6v^2+13v-8=-3

Solution for 6v^2+13v-8=-3 equation:

6v^2+13v-8=-3

We move all terms to the left:

6v^2+13v-8-(-3)=0

We add all the numbers together, and all the variables

6v^2+13v-5=0

a = 6; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·6·(-5)
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{-(13)-17}{2*6}=\frac{-30}{12}
=-2+1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+17}{2*6}=\frac{4}{12}
=1/3
$