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

Solution for 4/x+1=2/2x-3 equation:

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


8x/2x^2+(-2x)/2x^2+3+1=0

We add all the numbers together, and all the variables

8x/2x^2+(-2x)/2x^2+4=0

We multiply all the terms by the denominator


8x+(-2x)+4*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2+6x=0

a = 8; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·8·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*8}=\frac{-12}{16}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*8}=\frac{0}{16}
=0
$