2(x-9)(x-4)=0

Solution for 2(x-9)(x-4)=0 equation:

2(x-9)(x-4)=0

We multiply parentheses ..

2(+x^2-4x-9x+36)=0

We multiply parentheses

2x^2-8x-18x+72=0

We add all the numbers together, and all the variables

2x^2-26x+72=0

a = 2; b = -26; c = +72;
Δ = b2-4ac
Δ = -262-4·2·72
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-10}{2*2}=\frac{16}{4}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+10}{2*2}=\frac{36}{4}
=9
$