(5-2i)(-3+7i)=

Solution for (5-2i)(-3+7i)= equation:

(5-2i)(-3+7i)=

We move all terms to the left:

(5-2i)(-3+7i)-()=0

We add all the numbers together, and all the variables

(-2i+5)(7i-3)-()=0

We add all the numbers together, and all the variables

(-2i+5)(7i-3)=0

We multiply parentheses ..

(-14i^2+6i+35i-15)=0

We get rid of parentheses

-14i^2+6i+35i-15=0

We add all the numbers together, and all the variables

-14i^2+41i-15=0

a = -14; b = 41; c = -15;
Δ = b2-4ac
Δ = 412-4·(-14)·(-15)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-29}{2*-14}=\frac{-70}{-28}
=2+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+29}{2*-14}=\frac{-12}{-28}
=3/7
$