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

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

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

We multiply parentheses ..

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

We multiply parentheses

5x^2-20x-25x+100=0

We add all the numbers together, and all the variables

5x^2-45x+100=0

a = 5; b = -45; c = +100;
Δ = b2-4ac
Δ = -452-4·5·100
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5}{2*5}=\frac{40}{10}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5}{2*5}=\frac{50}{10}
=5
$