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

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

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

We move all terms to the left:

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


Domain of the equation: 8d!=0

d!=0/8

d!=0

d∈R



Domain of the equation: 6d+46)!=0

d∈R


We get rid of parentheses

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

We calculate fractions


18d/48d^2+(-40d)/48d^2-46+35=0

We add all the numbers together, and all the variables

18d/48d^2+(-40d)/48d^2-11=0

We multiply all the terms by the denominator


18d+(-40d)-11*48d^2=0

Wy multiply elements

-528d^2+18d+(-40d)=0

We get rid of parentheses

-528d^2+18d-40d=0

We add all the numbers together, and all the variables

-528d^2-22d=0

a = -528; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-528)·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*-528}=\frac{0}{-1056}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-528}=\frac{44}{-1056}
=-1/24
$