x+4/x+5=x-5/2x

Solution for x+4/x+5=x-5/2x equation:

x+4/x+5=x-5/2x

We move all terms to the left:

x+4/x+5-(x-5/2x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+4/x-(+x-5/2x)+5=0

We get rid of parentheses

x+4/x-x+5/2x+5=0

We calculate fractions


x-x+8x/2x^2+5x/2x^2+5=0

We add all the numbers together, and all the variables

8x/2x^2+5x/2x^2+5=0

We multiply all the terms by the denominator


8x+5x+5*2x^2=0

We add all the numbers together, and all the variables

13x+5*2x^2=0

Wy multiply elements

10x^2+13x=0

a = 10; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·10·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*10}=\frac{-26}{20}
=-1+3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*10}=\frac{0}{20}
=0
$