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

Solution for (2x-2)(x-9)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-20x+18=0

a = 2; b = -20; c = +18;
Δ = b2-4ac
Δ = -202-4·2·18
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16}{2*2}=\frac{36}{4}
=9
$