(6+i)(2+7i)=0

Solution for (6+i)(2+7i)=0 equation:

(6+i)(2+7i)=0

We add all the numbers together, and all the variables

(i+6)(7i+2)=0

We multiply parentheses ..

(+7i^2+2i+42i+12)=0

We get rid of parentheses

7i^2+2i+42i+12=0

We add all the numbers together, and all the variables

7i^2+44i+12=0

a = 7; b = 44; c = +12;
Δ = b2-4ac
Δ = 442-4·7·12
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-40}{2*7}=\frac{-84}{14}
=-6
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+40}{2*7}=\frac{-4}{14}
=-2/7
$