(x-2)(x-9)=-12

Solution for (x-2)(x-9)=-12 equation:

(x-2)(x-9)=-12

We move all terms to the left:

(x-2)(x-9)-(-12)=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+x^2-9x-2x+18)+12=0

We get rid of parentheses

x^2-9x-2x+18+12=0

We add all the numbers together, and all the variables

x^2-11x+30=0

a = 1; b = -11; c = +30;
Δ = b2-4ac
Δ = -112-4·1·30
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*1}=\frac{12}{2}
=6
$