v^2=-7+8v

Solution for v^2=-7+8v equation:

v^2=-7+8v

We move all terms to the left:

v^2-(-7+8v)=0

We add all the numbers together, and all the variables

v^2-(8v-7)=0

We get rid of parentheses

v^2-8v+7=0

a = 1; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·1·7
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6}{2*1}=\frac{2}{2}
=1
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6}{2*1}=\frac{14}{2}
=7
$