x/2x+4+3x=3

Solution for x/2x+4+3x=3 equation:

x/2x+4+3x=3

We move all terms to the left:

x/2x+4+3x-(3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+x/2x+1=0

We multiply all the terms by the denominator


3x*2x+x+1*2x=0

We add all the numbers together, and all the variables

x+3x*2x+1*2x=0

Wy multiply elements

6x^2+x+2x=0

We add all the numbers together, and all the variables

6x^2+3x=0

a = 6; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·6·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*6}=\frac{0}{12}
=0
$