2d+1/6=-6(1/3d+1)

Solution for 2d+1/6=-6(1/3d+1) equation:

2d+1/6=-6(1/3d+1)

We move all terms to the left:

2d+1/6-(-6(1/3d+1))=0


Domain of the equation: 3d+1))!=0

d∈R


We calculate fractions


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

Fractions to decimals

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

We multiply all the terms by the denominator


2d*3d+1*3d+()=0

We add all the numbers together, and all the variables

2d*3d+1*3d=0

Wy multiply elements

6d^2+3d=0

a = 6; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·6·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*6}=\frac{-6}{12}
=-1/2
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*6}=\frac{0}{12}
=0
$