2d=61/3d+1

Solution for 2d=61/3d+1 equation:

2d=61/3d+1

We move all terms to the left:

2d-(61/3d+1)=0


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

d∈R


We get rid of parentheses

2d-61/3d-1=0

We multiply all the terms by the denominator


2d*3d-1*3d-61=0

Wy multiply elements

6d^2-3d-61=0

a = 6; b = -3; c = -61;
Δ = b2-4ac
Δ = -32-4·6·(-61)
Δ = 1473
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{1473}}{2*6}=\frac{3-\sqrt{1473}}{12}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1473}}{2*6}=\frac{3+\sqrt{1473}}{12}
$