5v2=-13v-8

Solution for 5v2=-13v-8 equation:

5v^2=-13v-8

We move all terms to the left:

5v^2-(-13v-8)=0

We get rid of parentheses

5v^2+13v+8=0

a = 5; b = 13; c = +8;
Δ = b2-4ac
Δ = 132-4·5·8
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3}{2*5}=\frac{-16}{10}
=-1+3/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3}{2*5}=\frac{-10}{10}
=-1
$