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

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

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

We move all terms to the left:

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


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

d∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2d*3d+9*3d+1))-(62)=0

We add all the numbers together, and all the variables

2d*3d+9*3d=0

Wy multiply elements

6d^2+27d=0

a = 6; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·6·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*6}=\frac{-54}{12}
=-4+1/2
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*6}=\frac{0}{12}
=0
$