2(x-1)(x-3)=(5+5)(x-1)

Solution for 2(x-1)(x-3)=(5+5)(x-1) equation:

2(x-1)(x-3)=(5+5)(x-1)

We move all terms to the left:

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

We add all the numbers together, and all the variables

2(x-1)(x-3)-(10(x-1))=0

We multiply parentheses ..

2(+x^2-3x-1x+3)-(10(x-1))=0


We calculate terms in parentheses: -(10(x-1)), so:

10(x-1)

We multiply parentheses

10x-10

Back to the equation:

-(10x-10)


We multiply parentheses

2x^2-6x-2x-(10x-10)+6=0

We get rid of parentheses

2x^2-6x-2x-10x+10+6=0

We add all the numbers together, and all the variables

2x^2-18x+16=0

a = 2; b = -18; c = +16;
Δ = b2-4ac
Δ = -182-4·2·16
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{-(-18)-14}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+14}{2*2}=\frac{32}{4}
=8
$