x(x-2)+(x-2)-(x-2)(7x-9)=0

Solution for x(x-2)+(x-2)-(x-2)(7x-9)=0 equation:

x(x-2)+(x-2)-(x-2)(7x-9)=0

We multiply parentheses

x^2-2x+(x-2)-(x-2)(7x-9)=0

We get rid of parentheses

x^2-2x+x-(x-2)(7x-9)-2=0

We multiply parentheses ..

x^2-(+7x^2-9x-14x+18)-2x+x-2=0

We add all the numbers together, and all the variables

x^2-(+7x^2-9x-14x+18)-1x-2=0

We get rid of parentheses

x^2-7x^2+9x+14x-1x-18-2=0

We add all the numbers together, and all the variables

-6x^2+22x-20=0

a = -6; b = 22; c = -20;
Δ = b2-4ac
Δ = 222-4·(-6)·(-20)
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{-(22)-2}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2}{2*-6}=\frac{-20}{-12}
=1+2/3
$