(1-14i)(5-3i)=0

Solution for (1-14i)(5-3i)=0 equation:

(1-14i)(5-3i)=0

We add all the numbers together, and all the variables

(-14i+1)(-3i+5)=0

We multiply parentheses ..

(+42i^2-70i-3i+5)=0

We get rid of parentheses

42i^2-70i-3i+5=0

We add all the numbers together, and all the variables

42i^2-73i+5=0

a = 42; b = -73; c = +5;
Δ = b2-4ac
Δ = -732-4·42·5
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-73)-67}{2*42}=\frac{6}{84}
=1/14
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+67}{2*42}=\frac{140}{84}
=1+2/3
$