(x-9)(2x-6)=0

Solution for (x-9)(2x-6)=0 equation:

(x-9)(2x-6)=0

We multiply parentheses ..

(+2x^2-6x-18x+54)=0

We get rid of parentheses

2x^2-6x-18x+54=0

We add all the numbers together, and all the variables

2x^2-24x+54=0

a = 2; b = -24; c = +54;
Δ = b2-4ac
Δ = -242-4·2·54
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12}{2*2}=\frac{12}{4}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*2}=\frac{36}{4}
=9
$