X=(7-2i)(7-3i)

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

X=(7-2X)(7-3X)

We move all terms to the left:

X-((7-2X)(7-3X))=0

We add all the numbers together, and all the variables

X-((-2X+7)(-3X+7))=0

We multiply parentheses ..

-((+6X^2-14X-21X+49))+X=0


We calculate terms in parentheses: -((+6X^2-14X-21X+49)), so:

(+6X^2-14X-21X+49)

We get rid of parentheses

6X^2-14X-21X+49

We add all the numbers together, and all the variables

6X^2-35X+49

Back to the equation:

-(6X^2-35X+49)


We add all the numbers together, and all the variables

X-(6X^2-35X+49)=0

We get rid of parentheses

-6X^2+X+35X-49=0

We add all the numbers together, and all the variables

-6X^2+36X-49=0

a = -6; b = 36; c = -49;
Δ = b2-4ac
Δ = 362-4·(-6)·(-49)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{30}}{2*-6}=\frac{-36-2\sqrt{30}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{30}}{2*-6}=\frac{-36+2\sqrt{30}}{-12}
$