3x+2x+1/2x=100

Solution for 3x+2x+1/2x=100 equation:

3x+2x+1/2x=100

We move all terms to the left:

3x+2x+1/2x-(100)=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-100=0

We multiply all the terms by the denominator


5x*2x-100*2x+1=0

Wy multiply elements

10x^2-200x+1=0

a = 10; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·10·1
Δ = 39960
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:

$\sqrt{\Delta}=\sqrt{39960}=\sqrt{36*1110}=\sqrt{36}*\sqrt{1110}=6\sqrt{1110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-6\sqrt{1110}}{2*10}=\frac{200-6\sqrt{1110}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+6\sqrt{1110}}{2*10}=\frac{200+6\sqrt{1110}}{20}
$