3/4d-5/6=2/3d

Solution for 3/4d-5/6=2/3d equation:

3/4d-5/6=2/3d

We move all terms to the left:

3/4d-5/6-(2/3d)=0


Domain of the equation: 4d!=0

d!=0/4

d!=0

d∈R



Domain of the equation: 3d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

3/4d-(+2/3d)-5/6=0

We get rid of parentheses

3/4d-2/3d-5/6=0

We calculate fractions


(-180d^2)/432d^2+324d/432d^2+(-288d)/432d^2=0

We multiply all the terms by the denominator


(-180d^2)+324d+(-288d)=0

We get rid of parentheses

-180d^2+324d-288d=0

We add all the numbers together, and all the variables

-180d^2+36d=0

a = -180; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-180)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-180}=\frac{-72}{-360}
=1/5
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-180}=\frac{0}{-360}
=0
$