0=-5v^2-17v-12

Solution for 0=-5v^2-17v-12 equation:

0=-5v^2-17v-12

We move all terms to the left:

0-(-5v^2-17v-12)=0

We add all the numbers together, and all the variables

-(-5v^2-17v-12)=0

We get rid of parentheses

5v^2+17v+12=0

a = 5; b = 17; c = +12;
Δ = b2-4ac
Δ = 172-4·5·12
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{-(17)-7}{2*5}=\frac{-24}{10}
=-2+2/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*5}=\frac{-10}{10}
=-1
$