(-5i)(7+6i)-(3i)(-6-8i)=0

Solution for (-5i)(7+6i)-(3i)(-6-8i)=0 equation:

(-5i)(7+6i)-(3i)(-6-8i)=0

We add all the numbers together, and all the variables

(-5i)(6i+7)-3i(-8i-6)=0

We multiply parentheses

24i^2+(-5i)(6i+7)+18i=0

We multiply parentheses ..

24i^2+(-30i^2-35i)+18i=0

We get rid of parentheses

24i^2-30i^2-35i+18i=0

We add all the numbers together, and all the variables

-6i^2-17i=0

a = -6; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-6)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-6}=\frac{0}{-12}
=0
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-6}=\frac{34}{-12}
=-2+5/6
$