2x=3+1/2x

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

2x=3+1/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-1/2x-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-6x-1=0

a = 4; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·4·(-1)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*4}=\frac{6-2\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*4}=\frac{6+2\sqrt{13}}{8}
$