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

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

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


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

x∈R


We multiply parentheses ..

((+x^2+3x-7x-21))/((x-5)(x-5))=0

We multiply all the terms by the denominator


((+x^2+3x-7x-21))=0


We calculate terms in parentheses: +((+x^2+3x-7x-21)), so:

(+x^2+3x-7x-21)

We get rid of parentheses

x^2+3x-7x-21

We add all the numbers together, and all the variables

x^2-4x-21

Back to the equation:

+(x^2-4x-21)


We get rid of parentheses

x^2-4x-21=0

a = 1; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·1·(-21)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*1}=\frac{14}{2}
=7
$