(x-4)*(x-5)=20

Solution for (x-4)*(x-5)=20 equation:

(x-4)(x-5)=20

We move all terms to the left:

(x-4)(x-5)-(20)=0

We multiply parentheses ..

(+x^2-5x-4x+20)-20=0

We get rid of parentheses

x^2-5x-4x+20-20=0

We add all the numbers together, and all the variables

x^2-9x=0

a = 1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·1·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*1}=\frac{18}{2}
=9
$