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(-2-4i)(8+5i)+4i(-6-7i)=0
We add all the numbers together, and all the variables
(-4i-2)(5i+8)+4i(-7i-6)=0
We multiply parentheses
-28i^2+(-4i-2)(5i+8)-24i=0
We multiply parentheses ..
-28i^2+(-20i^2-32i-10i-16)-24i=0
We get rid of parentheses
-28i^2-20i^2-32i-10i-24i-16=0
We add all the numbers together, and all the variables
-48i^2-66i-16=0
a = -48; b = -66; c = -16;
Δ = b2-4ac
Δ = -662-4·(-48)·(-16)
Δ = 1284
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}$$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{321}}{2*-48}=\frac{66-2\sqrt{321}}{-96} $$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{321}}{2*-48}=\frac{66+2\sqrt{321}}{-96} $
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