5=(x-2)(x-3)

Solution for 5=(x-2)(x-3) equation:

5=(x-2)(x-3)

We move all terms to the left:

5-((x-2)(x-3))=0

We multiply parentheses ..

-((+x^2-3x-2x+6))+5=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 get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+5x-1=0

a = -1; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-1)·(-1)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{21}}{2*-1}=\frac{-5-\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{21}}{2*-1}=\frac{-5+\sqrt{21}}{-2}
$