-2/3i+5=20-i

Solution for -2/3i+5=20-i equation:

-2/3i+5=20-i

We move all terms to the left:

-2/3i+5-(20-i)=0


Domain of the equation: 3i!=0

i!=0/3

i!=0

i∈R


We add all the numbers together, and all the variables

-2/3i-(-1i+20)+5=0

We get rid of parentheses

-2/3i+1i-20+5=0

We multiply all the terms by the denominator


1i*3i-20*3i+5*3i-2=0

Wy multiply elements

3i^2-60i+15i-2=0

We add all the numbers together, and all the variables

3i^2-45i-2=0

a = 3; b = -45; c = -2;
Δ = b2-4ac
Δ = -452-4·3·(-2)
Δ = 2049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2049}}{2*3}=\frac{45-\sqrt{2049}}{6}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2049}}{2*3}=\frac{45+\sqrt{2049}}{6}
$