1/2x+2x=240

Solution for 1/2x+2x=240 equation:

1/2x+2x=240

We move all terms to the left:

1/2x+2x-(240)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x-240=0

We multiply all the terms by the denominator


2x*2x-240*2x+1=0

Wy multiply elements

4x^2-480x+1=0

a = 4; b = -480; c = +1;
Δ = b2-4ac
Δ = -4802-4·4·1
Δ = 230384
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:

$\sqrt{\Delta}=\sqrt{230384}=\sqrt{1936*119}=\sqrt{1936}*\sqrt{119}=44\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-44\sqrt{119}}{2*4}=\frac{480-44\sqrt{119}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+44\sqrt{119}}{2*4}=\frac{480+44\sqrt{119}}{8}
$