0=(x-9)(x-12)

Solution for 0=(x-9)(x-12) equation:

0=(x-9)(x-12)

We move all terms to the left:

0-((x-9)(x-12))=0

We add all the numbers together, and all the variables

-((x-9)(x-12))=0

We multiply parentheses ..

-((+x^2-12x-9x+108))=0


We calculate terms in parentheses: -((+x^2-12x-9x+108)), so:

(+x^2-12x-9x+108)

We get rid of parentheses

x^2-12x-9x+108

We add all the numbers together, and all the variables

x^2-21x+108

Back to the equation:

-(x^2-21x+108)


We get rid of parentheses

-x^2+21x-108=0

We add all the numbers together, and all the variables

-1x^2+21x-108=0

a = -1; b = 21; c = -108;
Δ = b2-4ac
Δ = 212-4·(-1)·(-108)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3}{2*-1}=\frac{-18}{-2}
=+9
$