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

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
$