v+23=15-7/v

Solution for v+23=15-7/v equation:

v+23=15-7/v

We move all terms to the left:

v+23-(15-7/v)=0


Domain of the equation: v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

v-(-7/v+15)+23=0

We get rid of parentheses

v+7/v-15+23=0

We multiply all the terms by the denominator


v*v-15*v+23*v+7=0

We add all the numbers together, and all the variables

8v+v*v+7=0

Wy multiply elements

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