2v^2=-5-7v

Solution for 2v^2=-5-7v equation:

2v^2=-5-7v

We move all terms to the left:

2v^2-(-5-7v)=0

We add all the numbers together, and all the variables

2v^2-(-7v-5)=0

We get rid of parentheses

2v^2+7v+5=0

a = 2; b = 7; c = +5;
Δ = b2-4ac
Δ = 72-4·2·5
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{-(7)-3}{2*2}=\frac{-10}{4}
=-2+1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*2}=\frac{-4}{4}
=-1
$