1/3d+8=1/6d-2

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Solution for 1/3d+8=1/6d-2 equation:



1/3d+8=1/6d-2
We move all terms to the left:
1/3d+8-(1/6d-2)=0
Domain of the equation: 3d!=0
d!=0/3
d!=0
d∈R
Domain of the equation: 6d-2)!=0
d∈R
We get rid of parentheses
1/3d-1/6d+2+8=0
We calculate fractions
6d/18d^2+(-3d)/18d^2+2+8=0
We add all the numbers together, and all the variables
6d/18d^2+(-3d)/18d^2+10=0
We multiply all the terms by the denominator
6d+(-3d)+10*18d^2=0
Wy multiply elements
180d^2+6d+(-3d)=0
We get rid of parentheses
180d^2+6d-3d=0
We add all the numbers together, and all the variables
180d^2+3d=0
a = 180; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·180·0
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*180}=\frac{-6}{360} =-1/60 $
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*180}=\frac{0}{360} =0 $

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