10/2x+4=4/x-5

Solution for 10/2x+4=4/x-5 equation:

10/2x+4=4/x-5

We move all terms to the left:

10/2x+4-(4/x-5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-5)!=0

x∈R


We get rid of parentheses

10/2x-4/x+5+4=0

We calculate fractions


10x/2x^2+(-8x)/2x^2+5+4=0

We add all the numbers together, and all the variables

10x/2x^2+(-8x)/2x^2+9=0

We multiply all the terms by the denominator


10x+(-8x)+9*2x^2=0

Wy multiply elements

18x^2+10x+(-8x)=0

We get rid of parentheses

18x^2+10x-8x=0

We add all the numbers together, and all the variables

18x^2+2x=0

a = 18; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·18·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*18}=\frac{-4}{36}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*18}=\frac{0}{36}
=0
$