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

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

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

We move all terms to the left:

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


Domain of the equation: 4i!=0

i!=0/4

i!=0

i∈R



Domain of the equation: 3i)!=0

i!=0/1

i!=0

i∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-180i^2+36i=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:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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