2(d-2)=12+2/3d

Solution for 2(d-2)=12+2/3d equation:

2(d-2)=12+2/3d

We move all terms to the left:

2(d-2)-(12+2/3d)=0


Domain of the equation: 3d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

2(d-2)-(2/3d+12)=0

We multiply parentheses

2d-(2/3d+12)-4=0

We get rid of parentheses

2d-2/3d-12-4=0

We multiply all the terms by the denominator


2d*3d-12*3d-4*3d-2=0

Wy multiply elements

6d^2-36d-12d-2=0

We add all the numbers together, and all the variables

6d^2-48d-2=0

a = 6; b = -48; c = -2;
Δ = b2-4ac
Δ = -482-4·6·(-2)
Δ = 2352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-28\sqrt{3}}{2*6}=\frac{48-28\sqrt{3}}{12}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+28\sqrt{3}}{2*6}=\frac{48+28\sqrt{3}}{12}
$