I(8-3i)(8+3i)=0

Solution for I(8-3i)(8+3i)=0 equation:

(8-3I)(8+3I)=0

We add all the numbers together, and all the variables

(-3I+8)(3I+8)=0

We multiply parentheses ..

(-9I^2-24I+24I+64)=0

We get rid of parentheses

-9I^2-24I+24I+64=0

We add all the numbers together, and all the variables

-9I^2+64=0

a = -9; b = 0; c = +64;
Δ = b2-4ac
Δ = 02-4·(-9)·64
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*-9}=\frac{-48}{-18}
=2+2/3
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*-9}=\frac{48}{-18}
=-2+2/3
$