(x-9)(4x-8)=0

Solution for (x-9)(4x-8)=0 equation:

(x-9)(4x-8)=0

We multiply parentheses ..

(+4x^2-8x-36x+72)=0

We get rid of parentheses

4x^2-8x-36x+72=0

We add all the numbers together, and all the variables

4x^2-44x+72=0

a = 4; b = -44; c = +72;
Δ = b2-4ac
Δ = -442-4·4·72
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-28}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+28}{2*4}=\frac{72}{8}
=9
$