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(14+-2i)(7+12i)=122+154i
We move all terms to the left:
(14+-2i)(7+12i)-(122+154i)=0
We add all the numbers together, and all the variables
(-2i)(12i+7)-(154i+122)=0
We get rid of parentheses
(-2i)(12i+7)-154i-122=0
We multiply parentheses ..
(-24i^2-14i)-154i-122=0
We get rid of parentheses
-24i^2-14i-154i-122=0
We add all the numbers together, and all the variables
-24i^2-168i-122=0
a = -24; b = -168; c = -122;
Δ = b2-4ac
Δ = -1682-4·(-24)·(-122)
Δ = 16512
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}$$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16512}=\sqrt{64*258}=\sqrt{64}*\sqrt{258}=8\sqrt{258}$$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-8\sqrt{258}}{2*-24}=\frac{168-8\sqrt{258}}{-48} $$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+8\sqrt{258}}{2*-24}=\frac{168+8\sqrt{258}}{-48} $
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