(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!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x+(2x-2)-2x*x=0

Wy multiply elements

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

We get rid of parentheses

-2x^2+3x+2x-2=0

We add all the numbers together, and all the variables

-2x^2+5x-2=0

a = -2; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·(-2)·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-2}=\frac{-2}{-4}
=1/2
$