(2+7i)(8+3i)=0

Solution for (2+7i)(8+3i)=0 equation:

(2+7i)(8+3i)=0

We add all the numbers together, and all the variables

(7i+2)(3i+8)=0

We multiply parentheses ..

(+21i^2+56i+6i+16)=0

We get rid of parentheses

21i^2+56i+6i+16=0

We add all the numbers together, and all the variables

21i^2+62i+16=0

a = 21; b = 62; c = +16;
Δ = b2-4ac
Δ = 622-4·21·16
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-50}{2*21}=\frac{-112}{42}
=-2+2/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+50}{2*21}=\frac{-12}{42}
=-2/7
$