(4+7i)(.5+2i)=0

Solution for (4+7i)(.5+2i)=0 equation:

(4+7i)(.5+2i)=0

We add all the numbers together, and all the variables

(7i+4)(2i+0.5)=0

We multiply parentheses ..

(+14i^2+3.5i+8i+2)=0

We get rid of parentheses

14i^2+3.5i+8i+2=0

We add all the numbers together, and all the variables

14i^2+11.5i+2=0

a = 14; b = 11.5; c = +2;
Δ = b2-4ac
Δ = 11.52-4·14·2
Δ = 20.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11.5)-\sqrt{20.25}}{2*14}=\frac{-11.5-\sqrt{20.25}}{28}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11.5)+\sqrt{20.25}}{2*14}=\frac{-11.5+\sqrt{20.25}}{28}
$