8/3d+35=5/6d=46

Solution for 8/3d+35=5/6d=46 equation:

8/3d+35=5/6d=46

We move all terms to the left:

8/3d+35-(5/6d)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 6d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

8/3d-(+5/6d)+35=0

We get rid of parentheses

8/3d-5/6d+35=0

We calculate fractions


48d/18d^2+(-15d)/18d^2+35=0

We multiply all the terms by the denominator


48d+(-15d)+35*18d^2=0

Wy multiply elements

630d^2+48d+(-15d)=0

We get rid of parentheses

630d^2+48d-15d=0

We add all the numbers together, and all the variables

630d^2+33d=0

a = 630; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·630·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*630}=\frac{-66}{1260}
=-11/210
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*630}=\frac{0}{1260}
=0
$