5/2x+3/x+1=7/x

Solution for 5/2x+3/x+1=7/x equation:

5/2x+3/x+1=7/x

We move all terms to the left:

5/2x+3/x+1-(7/x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 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

5/2x+3/x-(+7/x)+1=0

We get rid of parentheses

5/2x+3/x-7/x+1=0

We calculate fractions


5x/2x^2+(-14x+3)/2x^2+1=0

We multiply all the terms by the denominator


5x+(-14x+3)+1*2x^2=0

Wy multiply elements

2x^2+5x+(-14x+3)=0

We get rid of parentheses

2x^2+5x-14x+3=0

We add all the numbers together, and all the variables

2x^2-9x+3=0

a = 2; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·2·3
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{57}}{2*2}=\frac{9-\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*2}=\frac{9+\sqrt{57}}{4}
$