(-2+9i)(6+i)=0

Solution for (-2+9i)(6+i)=0 equation:

(-2+9i)(6+i)=0

We add all the numbers together, and all the variables

(9i-2)(i+6)=0

We multiply parentheses ..

(+9i^2+54i-2i-12)=0

We get rid of parentheses

9i^2+54i-2i-12=0

We add all the numbers together, and all the variables

9i^2+52i-12=0

a = 9; b = 52; c = -12;
Δ = b2-4ac
Δ = 522-4·9·(-12)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-56}{2*9}=\frac{-108}{18}
=-6
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+56}{2*9}=\frac{4}{18}
=2/9
$