(1-7i)(-6+7i)=0

Solution for (1-7i)(-6+7i)=0 equation:

(1-7i)(-6+7i)=0

We add all the numbers together, and all the variables

(-7i+1)(7i-6)=0

We multiply parentheses ..

(-49i^2+42i+7i-6)=0

We get rid of parentheses

-49i^2+42i+7i-6=0

We add all the numbers together, and all the variables

-49i^2+49i-6=0

a = -49; b = 49; c = -6;
Δ = b2-4ac
Δ = 492-4·(-49)·(-6)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-35}{2*-49}=\frac{-84}{-98}
=6/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+35}{2*-49}=\frac{-14}{-98}
=1/7
$