0=-4(x-5)(x-9)

Solution for 0=-4(x-5)(x-9) equation:

0=-4(x-5)(x-9)

We move all terms to the left:

0-(-4(x-5)(x-9))=0

We add all the numbers together, and all the variables

-(-4(x-5)(x-9))=0

We multiply parentheses ..

-(-4(+x^2-9x-5x+45))=0


We calculate terms in parentheses: -(-4(+x^2-9x-5x+45)), so:

-4(+x^2-9x-5x+45)

We multiply parentheses

-4x^2+36x+20x-180

We add all the numbers together, and all the variables

-4x^2+56x-180

Back to the equation:

-(-4x^2+56x-180)


We get rid of parentheses

4x^2-56x+180=0

a = 4; b = -56; c = +180;
Δ = b2-4ac
Δ = -562-4·4·180
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{-(-56)-16}{2*4}=\frac{40}{8}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+16}{2*4}=\frac{72}{8}
=9
$