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

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

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

We move all terms to the left:

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


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



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

d∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-36d^2+4d+(-3d)=0

We get rid of parentheses

-36d^2+4d-3d=0

We add all the numbers together, and all the variables

-36d^2+d=0

a = -36; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-36)·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*-36}=\frac{-2}{-72}
=1/36
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-36}=\frac{0}{-72}
=0
$