x+2x+1/2(3x)=3

Solution for x+2x+1/2(3x)=3 equation:

x+2x+1/2(3x)=3

We move all terms to the left:

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


Domain of the equation: 23x!=0

x!=0/23

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/23x-3=0

We multiply all the terms by the denominator


3x*23x-3*23x+1=0

Wy multiply elements

69x^2-69x+1=0

a = 69; b = -69; c = +1;
Δ = b2-4ac
Δ = -692-4·69·1
Δ = 4485
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-\sqrt{4485}}{2*69}=\frac{69-\sqrt{4485}}{138}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{4485}}{2*69}=\frac{69+\sqrt{4485}}{138}
$