4/x-5=5/2x

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

4/x-5=5/2x

We move all terms to the left:

4/x-5-(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

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


8x+(-5x)-5*2x^2=0

Wy multiply elements

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

We get rid of parentheses

-10x^2+8x-5x=0

We add all the numbers together, and all the variables

-10x^2+3x=0

a = -10; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-10)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-10}=\frac{-6}{-20}
=3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-10}=\frac{0}{-20}
=0
$