1/2x+3=4-2/x

Solution for 1/2x+3=4-2/x equation:

1/2x+3=4-2/x

We move all terms to the left:

1/2x+3-(4-2/x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-2/x+4)+3=0

We get rid of parentheses

1/2x+2/x-4+3=0

We calculate fractions


x/2x^2+4x/2x^2-4+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


x+4x-1*2x^2=0

We add all the numbers together, and all the variables

5x-1*2x^2=0

Wy multiply elements

-2x^2+5x=0

a = -2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-2)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-2}=\frac{0}{-4}
=0
$