(x-5)(2x-2)-(2x-2)=0

Solution for (x-5)(2x-2)-(2x-2)=0 equation:

(x-5)(2x-2)-(2x-2)=0

We get rid of parentheses

(x-5)(2x-2)-2x+2=0

We multiply parentheses ..

(+2x^2-2x-10x+10)-2x+2=0

We get rid of parentheses

2x^2-2x-10x-2x+10+2=0

We add all the numbers together, and all the variables

2x^2-14x+12=0

a = 2; b = -14; c = +12;
Δ = b2-4ac
Δ = -142-4·2·12
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{-(-14)-10}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*2}=\frac{24}{4}
=6
$