(2x-4)(x-7)=0

Solution for (2x-4)(x-7)=0 equation:

(2x-4)(x-7)=0

We multiply parentheses ..

(+2x^2-14x-4x+28)=0

We get rid of parentheses

2x^2-14x-4x+28=0

We add all the numbers together, and all the variables

2x^2-18x+28=0

a = 2; b = -18; c = +28;
Δ = b2-4ac
Δ = -182-4·2·28
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{-(-18)-10}{2*2}=\frac{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10}{2*2}=\frac{28}{4}
=7
$