5/x=2/2x-5

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

5/x=2/2x-5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


10x+(-2x)+5*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

10x^2+8x=0

a = 10; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·10·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*10}=\frac{-16}{20}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*10}=\frac{0}{20}
=0
$