4(x-5)(x-3)=0

Solution for 4(x-5)(x-3)=0 equation:

4(x-5)(x-3)=0

We multiply parentheses ..

4(+x^2-3x-5x+15)=0

We multiply parentheses

4x^2-12x-20x+60=0

We add all the numbers together, and all the variables

4x^2-32x+60=0

a = 4; b = -32; c = +60;
Δ = b2-4ac
Δ = -322-4·4·60
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8}{2*4}=\frac{24}{8}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8}{2*4}=\frac{40}{8}
=5
$