(2x-4)(x-6)=0

Solution for (2x-4)(x-6)=0 equation:

(2x-4)(x-6)=0

We multiply parentheses ..

(+2x^2-12x-4x+24)=0

We get rid of parentheses

2x^2-12x-4x+24=0

We add all the numbers together, and all the variables

2x^2-16x+24=0

a = 2; b = -16; c = +24;
Δ = b2-4ac
Δ = -162-4·2·24
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{-(-16)-8}{2*2}=\frac{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*2}=\frac{24}{4}
=6
$