32/d=12-d

Solution for 32/d=12-d equation:

32/d=12-d

We move all terms to the left:

32/d-(12-d)=0


Domain of the equation: d!=0

d∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

32/d+1d-12=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

d^2-12d+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:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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