3/2x-5=1/X+3

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

3x/2x^2+(-2x)/2x^2-8=0

We multiply all the terms by the denominator


3x+(-2x)-8*2x^2=0

Wy multiply elements

-16x^2+3x+(-2x)=0

We get rid of parentheses

-16x^2+3x-2x=0

We add all the numbers together, and all the variables

-16x^2+x=0

a = -16; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-16)·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*-16}=\frac{-2}{-32}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-16}=\frac{0}{-32}
=0
$