1/2x+2x=40

Solution for 1/2x+2x=40 equation:

1/2x+2x=40

We move all terms to the left:

1/2x+2x-(40)=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-40=0

We multiply all the terms by the denominator


2x*2x-40*2x+1=0

Wy multiply elements

4x^2-80x+1=0

a = 4; b = -80; c = +1;
Δ = b2-4ac
Δ = -802-4·4·1
Δ = 6384
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:

$\sqrt{\Delta}=\sqrt{6384}=\sqrt{16*399}=\sqrt{16}*\sqrt{399}=4\sqrt{399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{399}}{2*4}=\frac{80-4\sqrt{399}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{399}}{2*4}=\frac{80+4\sqrt{399}}{8}
$