x-6/x-3=2x/x-3*

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

x-6/x-3=2x/x-3*

We move all terms to the left:

x-6/x-3-(2x/x-3*)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-3*)!=0

x∈R


We add all the numbers together, and all the variables

x-6/x-(+2x/x)-3=0

We get rid of parentheses

x-6/x-2x/x-3=0

We multiply all the terms by the denominator


x*x-2x-3*x-6=0

We add all the numbers together, and all the variables

-5x+x*x-6=0

Wy multiply elements

x^2-5x-6=0

a = 1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*1}=\frac{12}{2}
=6
$