3-1/2d=3/2d+4-d

Solution for 3-1/2d=3/2d+4-d equation:

3-1/2d=3/2d+4-d

We move all terms to the left:

3-1/2d-(3/2d+4-d)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 2d+4-d)!=0

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

2d-d)!=-4

d∈R


We add all the numbers together, and all the variables

-1/2d-(-1d+3/2d+4)+3=0

We get rid of parentheses

-1/2d+1d-3/2d-4+3=0

We multiply all the terms by the denominator


1d*2d-4*2d+3*2d-1-3=0

We add all the numbers together, and all the variables

1d*2d-4*2d+3*2d-4=0

Wy multiply elements

2d^2-8d+6d-4=0

We add all the numbers together, and all the variables

2d^2-2d-4=0

a = 2; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·2·(-4)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*2}=\frac{-4}{4}
=-1
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*2}=\frac{8}{4}
=2
$