(x-20)(x-9)=0

Solution for (x-20)(x-9)=0 equation:

(x-20)(x-9)=0

We multiply parentheses ..

(+x^2-9x-20x+180)=0

We get rid of parentheses

x^2-9x-20x+180=0

We add all the numbers together, and all the variables

x^2-29x+180=0

a = 1; b = -29; c = +180;
Δ = b2-4ac
Δ = -292-4·1·180
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-11}{2*1}=\frac{18}{2}
=9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+11}{2*1}=\frac{40}{2}
=20
$