x-2/x-6=4/x-6

Solution for x-2/x-6=4/x-6 equation:

x-2/x-6=4/x-6

We move all terms to the left:

x-2/x-6-(4/x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-6)!=0

x∈R


We get rid of parentheses

x-2/x-4/x+6-6=0

We multiply all the terms by the denominator


x*x+6*x-6*x-2-4=0

We add all the numbers together, and all the variables

x*x-6=0

Wy multiply elements

x^2-6=0

a = 1; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·1·(-6)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*1}=\frac{0-2\sqrt{6}}{2}
=-\frac{2\sqrt{6}}{2}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*1}=\frac{0+2\sqrt{6}}{2}
=\frac{2\sqrt{6}}{2}
=\sqrt{6}
$