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}
$