1/2d-3=2/3d

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

1/2d-3=2/3d

We move all terms to the left:

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


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 3d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


3d/6d^2+(-4d)/6d^2-3=0

We multiply all the terms by the denominator


3d+(-4d)-3*6d^2=0

Wy multiply elements

-18d^2+3d+(-4d)=0

We get rid of parentheses

-18d^2+3d-4d=0

We add all the numbers together, and all the variables

-18d^2-1d=0

a = -18; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-18)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-18}=\frac{0}{-36}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-18}=\frac{2}{-36}
=-1/18
$