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

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

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

We move all terms to the left:

2/2x-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

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

We calculate fractions


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

We add all the numbers together, and all the variables

2x/2x^2+2x/2x^2-8=0

We multiply all the terms by the denominator


2x+2x-8*2x^2=0

We add all the numbers together, and all the variables

4x-8*2x^2=0

Wy multiply elements

-16x^2+4x=0

a = -16; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-16)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-16}=\frac{-8}{-32}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-16}=\frac{0}{-32}
=0
$