(x-2)(x-9)=18

Solution for (x-2)(x-9)=18 equation:

(x-2)(x-9)=18

We move all terms to the left:

(x-2)(x-9)-(18)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-11x=0

a = 1; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·1·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*1}=\frac{22}{2}
=11
$