((2x-2)/(x-5))=2x-8

Solution for ((2x-2)/(x-5))=2x-8 equation:

((2x-2)/(x-5))=2x-8

We move all terms to the left:

((2x-2)/(x-5))-(2x-8)=0


Domain of the equation: (x-5))!=0

x∈R


We get rid of parentheses

((2x-2)/(x-5))-2x+8=0

We multiply all the terms by the denominator


((2x-2)-2x*(x-5))+8*(x-5))=0


We calculate terms in parentheses: +((2x-2)-2x*(x-5)), so:

(2x-2)-2x*(x-5)

We multiply parentheses

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

We get rid of parentheses

-2x^2+2x+10x-2

We add all the numbers together, and all the variables

-2x^2+12x-2

Back to the equation:

+(-2x^2+12x-2)


We multiply parentheses

(-2x^2+12x-2)+8x+=0

We get rid of parentheses

-2x^2+12x+8x-2+=0

We add all the numbers together, and all the variables

-2x^2+20x=0

a = -2; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-2)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-2}=\frac{-40}{-4}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-2}=\frac{0}{-4}
=0
$