x-4/x-2=x+6+x+3=

Solution for x-4/x-2=x+6+x+3= equation:

x-4/x-2=x+6+x+3=

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-4/x-(2x+9)-2=0

We get rid of parentheses

x-4/x-2x-9-2=0

We multiply all the terms by the denominator


x*x-2x*x-9*x-2*x-4=0

We add all the numbers together, and all the variables

-11x+x*x-2x*x-4=0

Wy multiply elements

x^2-2x^2-11x-4=0

We add all the numbers together, and all the variables

-1x^2-11x-4=0

a = -1; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·(-1)·(-4)
Δ = 105
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{-(-11)-\sqrt{105}}{2*-1}=\frac{11-\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{105}}{2*-1}=\frac{11+\sqrt{105}}{-2}
$