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

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

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

We multiply parentheses ..

(+2x^2-6x-8x+24)=0

We get rid of parentheses

2x^2-6x-8x+24=0

We add all the numbers together, and all the variables

2x^2-14x+24=0

a = 2; b = -14; c = +24;
Δ = b2-4ac
Δ = -142-4·2·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2}{2*2}=\frac{12}{4}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*2}=\frac{16}{4}
=4
$