6v^2-3v-37=8

Solution for 6v^2-3v-37=8 equation:

6v^2-3v-37=8

We move all terms to the left:

6v^2-3v-37-(8)=0

We add all the numbers together, and all the variables

6v^2-3v-45=0

a = 6; b = -3; c = -45;
Δ = b2-4ac
Δ = -32-4·6·(-45)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-33}{2*6}=\frac{-30}{12}
=-2+1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+33}{2*6}=\frac{36}{12}
=3
$