-2i(-6+2i)+6(5-6i)=0

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Solution for -2i(-6+2i)+6(5-6i)=0 equation:



-2i(-6+2i)+6(5-6i)=0
We add all the numbers together, and all the variables
-2i(2i-6)+6(-6i+5)=0
We multiply parentheses
-4i^2+12i-36i+30=0
We add all the numbers together, and all the variables
-4i^2-24i+30=0
a = -4; b = -24; c = +30;
Δ = b2-4ac
Δ = -242-4·(-4)·30
Δ = 1056
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:
$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{66}}{2*-4}=\frac{24-4\sqrt{66}}{-8} $
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{66}}{2*-4}=\frac{24+4\sqrt{66}}{-8} $

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