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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2x*2x+1*2x+3))-((1+3))=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

2x*2x+1*2x=0

Wy multiply elements

4x^2+2x=0

a = 4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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