(7-5i)(8+6i)=0

Solution for (7-5i)(8+6i)=0 equation:

(7-5i)(8+6i)=0

We add all the numbers together, and all the variables

(-5i+7)(6i+8)=0

We multiply parentheses ..

(-30i^2-40i+42i+56)=0

We get rid of parentheses

-30i^2-40i+42i+56=0

We add all the numbers together, and all the variables

-30i^2+2i+56=0

a = -30; b = 2; c = +56;
Δ = b2-4ac
Δ = 22-4·(-30)·56
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-82}{2*-30}=\frac{-84}{-60}
=1+2/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+82}{2*-30}=\frac{80}{-60}
=-1+1/3
$