(x-7)(x-1)-(3x+5)(x-1)=0

Solution for (x-7)(x-1)-(3x+5)(x-1)=0 equation:

(x-7)(x-1)-(3x+5)(x-1)=0

We multiply parentheses ..

(+x^2-1x-7x+7)-(3x+5)(x-1)=0

We get rid of parentheses

x^2-1x-7x-(3x+5)(x-1)+7=0

We multiply parentheses ..

x^2-(+3x^2-3x+5x-5)-1x-7x+7=0

We add all the numbers together, and all the variables

x^2-(+3x^2-3x+5x-5)-8x+7=0

We get rid of parentheses

x^2-3x^2+3x-5x-8x+5+7=0

We add all the numbers together, and all the variables

-2x^2-10x+12=0

a = -2; b = -10; c = +12;
Δ = b2-4ac
Δ = -102-4·(-2)·12
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*-2}=\frac{24}{-4}
=-6
$