32/v=12-v

Solution for 32/v=12-v equation:

32/v=12-v

We move all terms to the left:

32/v-(12-v)=0


Domain of the equation: v!=0

v∈R


We add all the numbers together, and all the variables

32/v-(-1v+12)=0

We get rid of parentheses

32/v+1v-12=0

We multiply all the terms by the denominator


1v*v-12*v+32=0

We add all the numbers together, and all the variables

-12v+1v*v+32=0

Wy multiply elements

v^2-12v+32=0

a = 1; b = -12; c = +32;
Δ = b2-4ac
Δ = -122-4·1·32
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4}{2*1}=\frac{8}{2}
=4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*1}=\frac{16}{2}
=8
$