8/2d+35=5/6d+46

Solution for 8/2d+35=5/6d+46 equation:

8/2d+35=5/6d+46

We move all terms to the left:

8/2d+35-(5/6d+46)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



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

d∈R


We get rid of parentheses

8/2d-5/6d-46+35=0

We calculate fractions


48d/12d^2+(-10d)/12d^2-46+35=0

We add all the numbers together, and all the variables

48d/12d^2+(-10d)/12d^2-11=0

We multiply all the terms by the denominator


48d+(-10d)-11*12d^2=0

Wy multiply elements

-132d^2+48d+(-10d)=0

We get rid of parentheses

-132d^2+48d-10d=0

We add all the numbers together, and all the variables

-132d^2+38d=0

a = -132; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-132)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-132}=\frac{-76}{-264}
=19/66
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-132}=\frac{0}{-264}
=0
$