2x-9/x-4=x+4

Solution for 2x-9/x-4=x+4 equation:

2x-9/x-4=x+4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-8x+2x*x-x*x-9=0

Wy multiply elements

2x^2-1x^2-8x-9=0

We add all the numbers together, and all the variables

x^2-8x-9=0

a = 1; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·1·(-9)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*1}=\frac{18}{2}
=9
$