1/3d+1=5/6d-3

Solution for 1/3d+1=5/6d-3 equation:

1/3d+1=5/6d-3

We move all terms to the left:

1/3d+1-(5/6d-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-5/6d+3+1=0

We calculate fractions


6d/18d^2+(-15d)/18d^2+3+1=0

We add all the numbers together, and all the variables

6d/18d^2+(-15d)/18d^2+4=0

We multiply all the terms by the denominator


6d+(-15d)+4*18d^2=0

Wy multiply elements

72d^2+6d+(-15d)=0

We get rid of parentheses

72d^2+6d-15d=0

We add all the numbers together, and all the variables

72d^2-9d=0

a = 72; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·72·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*72}=\frac{0}{144}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*72}=\frac{18}{144}
=1/8
$