X=(7-3i)(6+i)

Solution for X=(7-3i)(6+i) equation:

X=(7-3X)(6+X)

We move all terms to the left:

X-((7-3X)(6+X))=0

We add all the numbers together, and all the variables

X-((-3X+7)(X+6))=0

We multiply parentheses ..

-((-3X^2-18X+7X+42))+X=0


We calculate terms in parentheses: -((-3X^2-18X+7X+42)), so:

(-3X^2-18X+7X+42)

We get rid of parentheses

-3X^2-18X+7X+42

We add all the numbers together, and all the variables

-3X^2-11X+42

Back to the equation:

-(-3X^2-11X+42)


We get rid of parentheses

3X^2+11X+X-42=0

We add all the numbers together, and all the variables

3X^2+12X-42=0

a = 3; b = 12; c = -42;
Δ = b2-4ac
Δ = 122-4·3·(-42)
Δ = 648
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18\sqrt{2}}{2*3}=\frac{-12-18\sqrt{2}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18\sqrt{2}}{2*3}=\frac{-12+18\sqrt{2}}{6}
$