(8-2i)(9=i)

Solution for (8-2i)(9=i) equation:

(8-2i)(9=i)

We move all terms to the left:

(8-2i)(9-(i))=0

We add all the numbers together, and all the variables

(-2i+8)(-1i+9)=0

We multiply parentheses ..

(+2i^2-18i-8i+72)=0

We get rid of parentheses

2i^2-18i-8i+72=0

We add all the numbers together, and all the variables

2i^2-26i+72=0

a = 2; b = -26; c = +72;
Δ = b2-4ac
Δ = -262-4·2·72
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-10}{2*2}=\frac{16}{4}
=4
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+10}{2*2}=\frac{36}{4}
=9
$