5/6d-5=-2/3d+3

Solution for 5/6d-5=-2/3d+3 equation:

5/6d-5=-2/3d+3

We move all terms to the left:

5/6d-5-(-2/3d+3)=0


Domain of the equation: 6d!=0

d!=0/6

d!=0

d∈R



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

d∈R


We get rid of parentheses

5/6d+2/3d-3-5=0

We calculate fractions


15d/18d^2+12d/18d^2-3-5=0

We add all the numbers together, and all the variables

15d/18d^2+12d/18d^2-8=0

We multiply all the terms by the denominator


15d+12d-8*18d^2=0

We add all the numbers together, and all the variables

27d-8*18d^2=0

Wy multiply elements

-144d^2+27d=0

a = -144; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-144)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-144}=\frac{-54}{-288}
=3/16
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-144}=\frac{0}{-288}
=0
$