2x(x-7)=2x-14

Solution for 2x(x-7)=2x-14 equation:

2x(x-7)=2x-14

We move all terms to the left:

2x(x-7)-(2x-14)=0

We multiply parentheses

2x^2-14x-(2x-14)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-16x+14=0

a = 2; b = -16; c = +14;
Δ = b2-4ac
Δ = -162-4·2·14
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12}{2*2}=\frac{28}{4}
=7
$