3+2x=1/2x+4

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

3+2x=1/2x+4

We move all terms to the left:

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


Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-8x+6x-1=0

We add all the numbers together, and all the variables

4x^2-2x-1=0

a = 4; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·4·(-1)
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*4}=\frac{2-2\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*4}=\frac{2+2\sqrt{5}}{8}
$