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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x*2x-3*2x+2=0

Wy multiply elements

4x^2-6x+2=0

a = 4; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·4·2
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*4}=\frac{8}{8}
=1
$