3x+2x+1/2x=20

Solution for 3x+2x+1/2x=20 equation:

3x+2x+1/2x=20

We move all terms to the left:

3x+2x+1/2x-(20)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/2x-20=0

We multiply all the terms by the denominator


5x*2x-20*2x+1=0

Wy multiply elements

10x^2-40x+1=0

a = 10; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·10·1
Δ = 1560
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:

$\sqrt{\Delta}=\sqrt{1560}=\sqrt{4*390}=\sqrt{4}*\sqrt{390}=2\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{390}}{2*10}=\frac{40-2\sqrt{390}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{390}}{2*10}=\frac{40+2\sqrt{390}}{20}
$