3x-9/x-3=3

Solution for 3x-9/x-3=3 equation:

3x-9/x-3=3

We move all terms to the left:

3x-9/x-3-(3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-9/x-6=0

We multiply all the terms by the denominator


3x*x-6*x-9=0

We add all the numbers together, and all the variables

-6x+3x*x-9=0

Wy multiply elements

3x^2-6x-9=0

a = 3; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·3·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*3}=\frac{18}{6}
=3
$