(7-5i)(7+9i)=0

Solution for (7-5i)(7+9i)=0 equation:

(7-5i)(7+9i)=0

We add all the numbers together, and all the variables

(-5i+7)(9i+7)=0

We multiply parentheses ..

(-45i^2-35i+63i+49)=0

We get rid of parentheses

-45i^2-35i+63i+49=0

We add all the numbers together, and all the variables

-45i^2+28i+49=0

a = -45; b = 28; c = +49;
Δ = b2-4ac
Δ = 282-4·(-45)·49
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-98}{2*-45}=\frac{-126}{-90}
=1+2/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+98}{2*-45}=\frac{70}{-90}
=-7/9
$