X-3x/x-2=6-6/x-2

Solution for X-3x/x-2=6-6/x-2 equation:

X-3X/X-2=6-6/X-2

We move all terms to the left:

X-3X/X-2-(6-6/X-2)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X-2)!=0

X∈R


We add all the numbers together, and all the variables

X-3X/X-(-6/X+4)-2=0

We get rid of parentheses

X-3X/X+6/X-4-2=0

We multiply all the terms by the denominator


X*X-3X-4*X-2*X+6=0

We add all the numbers together, and all the variables

-9X+X*X+6=0

Wy multiply elements

X^2-9X+6=0

a = 1; b = -9; c = +6;
Δ = b2-4ac
Δ = -92-4·1·6
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{57}}{2*1}=\frac{9-\sqrt{57}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*1}=\frac{9+\sqrt{57}}{2}
$