3-0.5d=3/2d+4-d

Solution for 3-0.5d=3/2d+4-d equation:

3-0.5d=3/2d+4-d

We move all terms to the left:

3-0.5d-(3/2d+4-d)=0


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

-0.5d-(-1d+3/2d+4)+3=0

We get rid of parentheses

-0.5d+1d-3/2d-4+3=0

We multiply all the terms by the denominator


-(0.5d)*2d+1d*2d-4*2d+3*2d-3=0

We add all the numbers together, and all the variables

-(+0.5d)*2d+1d*2d-4*2d+3*2d-3=0

We multiply parentheses

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

Wy multiply elements

-0d^2+2d^2-8d+6d-3=0

We add all the numbers together, and all the variables

d^2-2d-3=0

a = 1; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·1·(-3)
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{-(-2)-4}{2*1}=\frac{-2}{2}
=-1
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*1}=\frac{6}{2}
=3
$