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(7-6i)(-8+3i)=38-69i
We move all terms to the left:
(7-6i)(-8+3i)-(38-69i)=0
We add all the numbers together, and all the variables
(-6i+7)(3i-8)-(-69i+38)=0
We get rid of parentheses
(-6i+7)(3i-8)+69i-38=0
We multiply parentheses ..
(-18i^2+48i+21i-56)+69i-38=0
We get rid of parentheses
-18i^2+48i+21i+69i-56-38=0
We add all the numbers together, and all the variables
-18i^2+138i-94=0
a = -18; b = 138; c = -94;
Δ = b2-4ac
Δ = 1382-4·(-18)·(-94)
Δ = 12276
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}$$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12276}=\sqrt{36*341}=\sqrt{36}*\sqrt{341}=6\sqrt{341}$$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(138)-6\sqrt{341}}{2*-18}=\frac{-138-6\sqrt{341}}{-36} $$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(138)+6\sqrt{341}}{2*-18}=\frac{-138+6\sqrt{341}}{-36} $
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