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

Solution for (1/x)-3=5/2x+3 equation:

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

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+2x+(-5x)=0

We get rid of parentheses

-12x^2+2x-5x=0

We add all the numbers together, and all the variables

-12x^2-3x=0

a = -12; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-12)·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*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-12}=\frac{6}{-24}
=-1/4
$