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

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

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

We move all terms to the left:

8/3d+35-(6/5d+46)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 5d+46)!=0

d∈R


We get rid of parentheses

8/3d-6/5d-46+35=0

We calculate fractions


40d/15d^2+(-18d)/15d^2-46+35=0

We add all the numbers together, and all the variables

40d/15d^2+(-18d)/15d^2-11=0

We multiply all the terms by the denominator


40d+(-18d)-11*15d^2=0

Wy multiply elements

-165d^2+40d+(-18d)=0

We get rid of parentheses

-165d^2+40d-18d=0

We add all the numbers together, and all the variables

-165d^2+22d=0

a = -165; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-165)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-165}=\frac{-44}{-330}
=2/15
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-165}=\frac{0}{-330}
=0
$