i+23-2i=100/10i

Solution for i+23-2i=100/10i equation:

i+23-2i=100/10i

We move all terms to the left:

i+23-2i-(100/10i)=0


Domain of the equation: 10i)!=0

i!=0/1

i!=0

i∈R


We add all the numbers together, and all the variables

i-2i-(+100/10i)+23=0

We add all the numbers together, and all the variables

-1i-(+100/10i)+23=0

We get rid of parentheses

-1i-100/10i+23=0

We multiply all the terms by the denominator


-1i*10i+23*10i-100=0

Wy multiply elements

-10i^2+230i-100=0

a = -10; b = 230; c = -100;
Δ = b2-4ac
Δ = 2302-4·(-10)·(-100)
Δ = 48900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48900}=\sqrt{100*489}=\sqrt{100}*\sqrt{489}=10\sqrt{489}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(230)-10\sqrt{489}}{2*-10}=\frac{-230-10\sqrt{489}}{-20}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(230)+10\sqrt{489}}{2*-10}=\frac{-230+10\sqrt{489}}{-20}
$