X=(x-2)(x-3)

Solution for X=(x-2)(x-3) equation:

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

We move all terms to the left:

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

We multiply parentheses ..

-((+X^2-3X-2X+6))+X=0


We calculate terms in parentheses: -((+X^2-3X-2X+6)), so:

(+X^2-3X-2X+6)

We get rid of parentheses

X^2-3X-2X+6

We add all the numbers together, and all the variables

X^2-5X+6

Back to the equation:

-(X^2-5X+6)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1X^2+6X-6=0

a = -1; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·(-1)·(-6)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3}}{2*-1}=\frac{-6-2\sqrt{3}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3}}{2*-1}=\frac{-6+2\sqrt{3}}{-2}
$