3d+1/6=9(1/3d+2)

Solution for 3d+1/6=9(1/3d+2) equation:

3d+1/6=9(1/3d+2)

We move all terms to the left:

3d+1/6-(9(1/3d+2))=0


Domain of the equation: 3d+2))!=0

d∈R


We calculate fractions


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

Fractions to decimals

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

9d^2+3d=0

a = 9; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·9·0
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*9}=\frac{-6}{18}
=-1/3
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*9}=\frac{0}{18}
=0
$