4+1/x=10/2x

Solution for 4+1/x=10/2x equation:

4+1/x=10/2x

We move all terms to the left:

4+1/x-(10/2x)=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

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


2x+(-10x)+4*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-8x=0

a = 8; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·8·0
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*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*8}=\frac{16}{16}
=1
$