(5+i)(8+i)=0

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Solution for (5+i)(8+i)=0 equation:



(5+i)(8+i)=0
We add all the numbers together, and all the variables
(i+5)(i+8)=0
We multiply parentheses ..
(+i^2+8i+5i+40)=0
We get rid of parentheses
i^2+8i+5i+40=0
We add all the numbers together, and all the variables
i^2+13i+40=0
a = 1; b = 13; c = +40;
Δ = b2-4ac
Δ = 132-4·1·40
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3}{2*1}=\frac{-16}{2} =-8 $
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3}{2*1}=\frac{-10}{2} =-5 $

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