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

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

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

We move all terms to the left:

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


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-12d^2)/24d^2+8d/24d^2+(-12d)/24d^2=0

We multiply all the terms by the denominator


(-12d^2)+8d+(-12d)=0

We get rid of parentheses

-12d^2+8d-12d=0

We add all the numbers together, and all the variables

-12d^2-4d=0

a = -12; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-12)·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*-12}=\frac{0}{-24}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-12}=\frac{8}{-24}
=-1/3
$