(8+7i)(7+i)=0

Solution for (8+7i)(7+i)=0 equation:

(8+7i)(7+i)=0

We add all the numbers together, and all the variables

(7i+8)(i+7)=0

We multiply parentheses ..

(+7i^2+49i+8i+56)=0

We get rid of parentheses

7i^2+49i+8i+56=0

We add all the numbers together, and all the variables

7i^2+57i+56=0

a = 7; b = 57; c = +56;
Δ = b2-4ac
Δ = 572-4·7·56
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-41}{2*7}=\frac{-98}{14}
=-7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+41}{2*7}=\frac{-16}{14}
=-1+1/7
$