12x+1=1/2x

Solution for 12x+1=1/2x equation:

12x+1=1/2x

We move all terms to the left:

12x+1-(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

12x-(+1/2x)+1=0

We get rid of parentheses

12x-1/2x+1=0

We multiply all the terms by the denominator


12x*2x+1*2x-1=0

Wy multiply elements

24x^2+2x-1=0

a = 24; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·24·(-1)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*24}=\frac{-12}{48}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*24}=\frac{8}{48}
=1/6
$