1/3d+8=1/6d-3

Solution for 1/3d+8=1/6d-3 equation:

1/3d+8=1/6d-3

We move all terms to the left:

1/3d+8-(1/6d-3)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 6d-3)!=0

d∈R


We get rid of parentheses

1/3d-1/6d+3+8=0

We calculate fractions


6d/18d^2+(-3d)/18d^2+3+8=0

We add all the numbers together, and all the variables

6d/18d^2+(-3d)/18d^2+11=0

We multiply all the terms by the denominator


6d+(-3d)+11*18d^2=0

Wy multiply elements

198d^2+6d+(-3d)=0

We get rid of parentheses

198d^2+6d-3d=0

We add all the numbers together, and all the variables

198d^2+3d=0

a = 198; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·198·0
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*198}=\frac{-6}{396}
=-1/66
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*198}=\frac{0}{396}
=0
$