(x-9)(x+1)/(x-2)=0

Solution for (x-9)(x+1)/(x-2)=0 equation:

(x-9)(x+1)/(x-2)=0


Domain of the equation: (x-2)!=0

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

x!=2

x∈R


We multiply parentheses ..

(+x^2+x-9x-9)/(x-2)=0

We multiply all the terms by the denominator


(+x^2+x-9x-9)=0

We get rid of parentheses

x^2+x-9x-9=0

We add all the numbers together, and all the variables

x^2-8x-9=0

a = 1; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·1·(-9)
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{-(-8)-10}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*1}=\frac{18}{2}
=9
$