2x-1/2x=120

Solution for 2x-1/2x=120 equation:

2x-1/2x=120

We move all terms to the left:

2x-1/2x-(120)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-120*2x-1=0

Wy multiply elements

4x^2-240x-1=0

a = 4; b = -240; c = -1;
Δ = b2-4ac
Δ = -2402-4·4·(-1)
Δ = 57616
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:

$\sqrt{\Delta}=\sqrt{57616}=\sqrt{16*3601}=\sqrt{16}*\sqrt{3601}=4\sqrt{3601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-4\sqrt{3601}}{2*4}=\frac{240-4\sqrt{3601}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+4\sqrt{3601}}{2*4}=\frac{240+4\sqrt{3601}}{8}
$