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

Solution for ((2x-5)-(2x-5)(x-5))/(x-5)=0 equation:

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


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

We move all terms containing x to the left, all other terms to the right

x!=5

x∈R


We multiply parentheses ..

((2x-5)-(+2x^2-10x-5x+25))/(x-5)=0

We multiply all the terms by the denominator


((2x-5)-(+2x^2-10x-5x+25))=0


We calculate terms in parentheses: +((2x-5)-(+2x^2-10x-5x+25)), so:

(2x-5)-(+2x^2-10x-5x+25)

determiningTheFunctionDomain
-(+2x^2-10x-5x+25)+(2x-5)

We get rid of parentheses

-2x^2+10x+5x+2x-25-5

We add all the numbers together, and all the variables

-2x^2+17x-30

Back to the equation:

+(-2x^2+17x-30)


We get rid of parentheses

-2x^2+17x-30=0

a = -2; b = 17; c = -30;
Δ = b2-4ac
Δ = 172-4·(-2)·(-30)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*-2}=\frac{-10}{-4}
=2+1/2
$