6/3d-6+2/d-2=2/3

Solution for 6/3d-6+2/d-2=2/3 equation:

6/3d-6+2/d-2=2/3

We move all terms to the left:

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


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: d!=0

d∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


6d/27d^2+54d/27d^2+(-2d)/27d^2-8=0

We multiply all the terms by the denominator


6d+54d+(-2d)-8*27d^2=0

We add all the numbers together, and all the variables

60d+(-2d)-8*27d^2=0

Wy multiply elements

-216d^2+60d+(-2d)=0

We get rid of parentheses

-216d^2+60d-2d=0

We add all the numbers together, and all the variables

-216d^2+58d=0

a = -216; b = 58; c = 0;
Δ = b2-4ac
Δ = 582-4·(-216)·0
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-58}{2*-216}=\frac{-116}{-432}
=29/108
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+58}{2*-216}=\frac{0}{-432}
=0
$