(-9-4i)(5-2i)=0

Solution for (-9-4i)(5-2i)=0 equation:

(-9-4i)(5-2i)=0

We add all the numbers together, and all the variables

(-4i-9)(-2i+5)=0

We multiply parentheses ..

(+8i^2-20i+18i-45)=0

We get rid of parentheses

8i^2-20i+18i-45=0

We add all the numbers together, and all the variables

8i^2-2i-45=0

a = 8; b = -2; c = -45;
Δ = b2-4ac
Δ = -22-4·8·(-45)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-38}{2*8}=\frac{-36}{16}
=-2+1/4
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+38}{2*8}=\frac{40}{16}
=2+1/2
$