(1)/(2)d=(2)/(3)d-8

Solution for (1)/(2)d=(2)/(3)d-8 equation:

(1)/(2)d=(2)/(3)d-8

We move all terms to the left:

(1)/(2)d-((2)/(3)d-8)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 3d-8)!=0

d∈R


We get rid of parentheses

1/2d-2/3d+8=0

We calculate fractions


3d/6d^2+(-4d)/6d^2+8=0

We multiply all the terms by the denominator


3d+(-4d)+8*6d^2=0

Wy multiply elements

48d^2+3d+(-4d)=0

We get rid of parentheses

48d^2+3d-4d=0

We add all the numbers together, and all the variables

48d^2-1d=0

a = 48; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·48·0
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*48}=\frac{0}{96}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*48}=\frac{2}{96}
=1/48
$