(3/x)-(5/2x)=7

Solution for (3/x)-(5/2x)=7 equation:

(3/x)-(5/2x)=7

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

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

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

We get rid of parentheses

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

We calculate fractions


6x/2x^2+(-5x)/2x^2-7=0

We multiply all the terms by the denominator


6x+(-5x)-7*2x^2=0

Wy multiply elements

-14x^2+6x+(-5x)=0

We get rid of parentheses

-14x^2+6x-5x=0

We add all the numbers together, and all the variables

-14x^2+x=0

a = -14; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-14)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-14}=\frac{-2}{-28}
=1/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-14}=\frac{0}{-28}
=0
$