(D-e)/(3D+e)=e

Solution for (D-e)/(3D+e)=e equation:

(-D)/(3+D)=D

We move all terms to the left:

(-D)/(3+D)-(D)=0


Domain of the equation: (3+D)!=0

We move all terms containing D to the left, all other terms to the right

D!=-3

D∈R


We add all the numbers together, and all the variables

(-1D)/(D+3)-D=0

We add all the numbers together, and all the variables

-1D+(-1D)/(D+3)=0

We multiply all the terms by the denominator


-1D*(D+3)+(-1D)=0

We multiply parentheses

-D^2-3D+(-1D)=0

We get rid of parentheses

-D^2-3D-1D=0

We add all the numbers together, and all the variables

-1D^2-4D=0

a = -1; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-1)·0
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{-(-4)-4}{2*-1}=\frac{0}{-2}
=0
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-1}=\frac{8}{-2}
=-4
$