X=(5-2i)(1+3i)

Solution for X=(5-2i)(1+3i) equation:

X=(5-2X)(1+3X)

We move all terms to the left:

X-((5-2X)(1+3X))=0

We add all the numbers together, and all the variables

X-((-2X+5)(3X+1))=0

We multiply parentheses ..

-((-6X^2-2X+15X+5))+X=0


We calculate terms in parentheses: -((-6X^2-2X+15X+5)), so:

(-6X^2-2X+15X+5)

We get rid of parentheses

-6X^2-2X+15X+5

We add all the numbers together, and all the variables

-6X^2+13X+5

Back to the equation:

-(-6X^2+13X+5)


We get rid of parentheses

6X^2-13X+X-5=0

We add all the numbers together, and all the variables

6X^2-12X-5=0

a = 6; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·6·(-5)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*6}=\frac{12-2\sqrt{66}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*6}=\frac{12+2\sqrt{66}}{12}
$