5v^2=-1-10v

Solution for 5v^2=-1-10v equation:

5v^2=-1-10v

We move all terms to the left:

5v^2-(-1-10v)=0

We add all the numbers together, and all the variables

5v^2-(-10v-1)=0

We get rid of parentheses

5v^2+10v+1=0

a = 5; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·5·1
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{5}}{2*5}=\frac{-10-4\sqrt{5}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{5}}{2*5}=\frac{-10+4\sqrt{5}}{10}
$