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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-8i^2+34i-21=0

a = -8; b = 34; c = -21;
Δ = b2-4ac
Δ = 342-4·(-8)·(-21)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-22}{2*-8}=\frac{-56}{-16}
=3+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+22}{2*-8}=\frac{-12}{-16}
=3/4
$