((x-6)(x+5))/((x-9)^7)=0

Solution for ((x-6)(x+5))/((x-9)^7)=0 equation:

((x-6)(x+5))/((x-9)^7)=0


Domain of the equation: ((x-9)^7)!=0

x∈R


We multiply parentheses ..

((+x^2+5x-6x-30))/((x-9)^7)=0

We multiply all the terms by the denominator


((+x^2+5x-6x-30))=0


We calculate terms in parentheses: +((+x^2+5x-6x-30)), so:

(+x^2+5x-6x-30)

We get rid of parentheses

x^2+5x-6x-30

We add all the numbers together, and all the variables

x^2-1x-30

Back to the equation:

+(x^2-1x-30)


We get rid of parentheses

x^2-1x-30=0

a = 1; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·1·(-30)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*1}=\frac{12}{2}
=6
$