4x+2=1/2x+1

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

4x+2=1/2x+1

We move all terms to the left:

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


Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


4x*2x-1*2x+2*2x-1=0

Wy multiply elements

8x^2-2x+4x-1=0

We add all the numbers together, and all the variables

8x^2+2x-1=0

a = 8; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·8·(-1)
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{-(2)-6}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*8}=\frac{4}{16}
=1/4
$