10/x+8=14/2x-5

Solution for 10/x+8=14/2x-5 equation:

10/x+8=14/2x-5

We move all terms to the left:

10/x+8-(14/2x-5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

10/x-14/2x+5+8=0

We calculate fractions


20x/2x^2+(-14x)/2x^2+5+8=0

We add all the numbers together, and all the variables

20x/2x^2+(-14x)/2x^2+13=0

We multiply all the terms by the denominator


20x+(-14x)+13*2x^2=0

Wy multiply elements

26x^2+20x+(-14x)=0

We get rid of parentheses

26x^2+20x-14x=0

We add all the numbers together, and all the variables

26x^2+6x=0

a = 26; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·26·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*26}=\frac{-12}{52}
=-3/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*26}=\frac{0}{52}
=0
$