1/2x+12x=5

Solution for 1/2x+12x=5 equation:

1/2x+12x=5

We move all terms to the left:

1/2x+12x-(5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

12x+1/2x-5=0

We multiply all the terms by the denominator


12x*2x-5*2x+1=0

Wy multiply elements

24x^2-10x+1=0

a = 24; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·24·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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