(3-4i)(2+7i)=0

Solution for (3-4i)(2+7i)=0 equation:

(3-4i)(2+7i)=0

We add all the numbers together, and all the variables

(-4i+3)(7i+2)=0

We multiply parentheses ..

(-28i^2-8i+21i+6)=0

We get rid of parentheses

-28i^2-8i+21i+6=0

We add all the numbers together, and all the variables

-28i^2+13i+6=0

a = -28; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·(-28)·6
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-29}{2*-28}=\frac{-42}{-56}
=3/4
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+29}{2*-28}=\frac{16}{-56}
=-2/7
$