(x-5)(x-15)=0

Solution for (x-5)(x-15)=0 equation:

(x-5)(x-15)=0

We multiply parentheses ..

(+x^2-15x-5x+75)=0

We get rid of parentheses

x^2-15x-5x+75=0

We add all the numbers together, and all the variables

x^2-20x+75=0

a = 1; b = -20; c = +75;
Δ = b2-4ac
Δ = -202-4·1·75
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{-(-20)-10}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10}{2*1}=\frac{30}{2}
=15
$