5i(-6+9i)=0

Solution for 5i(-6+9i)=0 equation:

5i(-6+9i)=0

We add all the numbers together, and all the variables

5i(9i-6)=0

We multiply parentheses

45i^2-30i=0

a = 45; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·45·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*45}=\frac{0}{90}
=0
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*45}=\frac{60}{90}
=2/3
$