8/3i+2/9i=44

Solution for 8/3i+2/9i=44 equation:

8/3i+2/9i=44

We move all terms to the left:

8/3i+2/9i-(44)=0


Domain of the equation: 3i!=0

i!=0/3

i!=0

i∈R



Domain of the equation: 9i!=0

i!=0/9

i!=0

i∈R


We calculate fractions


72i/27i^2+6i/27i^2-44=0

We multiply all the terms by the denominator


72i+6i-44*27i^2=0

We add all the numbers together, and all the variables

78i-44*27i^2=0

Wy multiply elements

-1188i^2+78i=0

a = -1188; b = 78; c = 0;
Δ = b2-4ac
Δ = 782-4·(-1188)·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-78}{2*-1188}=\frac{-156}{-2376}
=13/198
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+78}{2*-1188}=\frac{0}{-2376}
=0
$